Important Note: In all scenarios below it is forbidden due to the cooking restrictions to place the item in an area where it can reach Yad Soledes. The below discussion is only with regards to if melting the item to less than Yad Soledes contains a Nolad prohibition. See “The Laws of Cooking” for further reference on the cooking prohibition!
A. Placing congealed fat in an area where it will melt:
Note: This Halacha was already fully discussed in “The Laws of Cooking” Halacha 8. See there for the full discussion on this topic.
The First Opinion
Foods which are filled with pieces of congealed fat are forbidden to be heated up even at a distance from the fire which is even in a place where [the food will] not [be able to get heated top the point of] Yad Soledes.
The reason for the above restriction is:  because the congealed fat that is inside [the food] melts [in the heat] and doing so is similar to [one] crushing a piece of ice in order to liquefy it, in which case the Sages prohibited [one from doing so] being that [through doing so] one is creating [a new substance] on Shabbos which is similar to a
forbidden action being that he is creating this water [from the ice] as will be explained in the next Halacha regarding placing ice near a source of heat. This same decree applies as well to dissolving fat.
The law if the fat will melt into the food and will thus not be recognizable: However the above [prohibition to melt the fat] only refers to when so much fat has melted that it oozes out [of the pastry], and is its own substance. [Meaning] that it is not mixed into any other food and is [thus] recognizable on its own. However if it has been left such a great distance [from the fire] that not enough fat will melt for it to ooze out [of the pastry], and rather only a slight amount of it will melt and will get absorbed into the pastry itself and [will thus] not be visible on its own, then it is allowed to [be placed there] even initially just like it is allowed to place a piece of ice in a cup of wine despite that the ice will melt into it, being that [the melted water] will get mixed and nullified within the wine in the cup, and is [thus] not a separate substance as was explained above.
[Furthermore] even if a small amount of [the fat] does flow out [of the pastry] and is [recognizable as] a substance of its own, [nevertheless] since it is a small amount it is not given any [Halachic] importance and is permitted.
Melting fat in the sun:  In all cases that it is forbidden to heat up a food with congealed fat [it is] even [forbidden] to do so by leaving it in the sun.
If the fat melted on Shabbos it may not be eaten:  If [the fat] already [melted] then the fat that had melted on Shabbos is forbidden [to be eaten].
The reason for this is: as this is the law with juice that has flowed on Shabbos from fruits that are designated to be used for juice which are forbidden [to be drunk] due to a decree that [if this were to be allowed then] one may come to squeeze the fruits on Shabbos [in order to make juice] being that these [fruits] are designated for this purpose as will be explained there [in chapter 320 Halacha 3]. This [suspicion] likewise applies to this fat [that has melted on Shabbos] as since it is common for [the fat] to be liquidly and transparent therefore when it is congealed it is similar to fruits that are designated to be juiced, of which the juice that flows from it on Shabbos is forbidden until night [i.e. after Shabbos].
The Second Opinion:
However there are opinions which argue on all this and say that there is no prohibition at all in melting fat through placing it in a hot area, as the [Sages] only prohibited breaking [and thus dissolving] a piece of ice with ones hands, however to let it dissolve on its own there is no decree [against doing so].
The Final Ruling in Shulchan Aruch:
Concerning the final ruling the custom is to initially be stringent like the first opinion although once the fat has already melted one may be lenient like the second opinion. [Furthermore] even initially one may rely on the second opinion in a time of need, being that this is the main Halachic opinion.
Placing the fat on top of a heater that is not yet lit: As well one may be lenient to place pastries filled with fat onto a heater before it is lit and have it consequently melt when the gentile lights the heater.
The reason for this is: because [in this scenario] even regarding the cooking prohibition, [meaning if one were to place there] a food which has a cooking prohibition applicable to it, [cooking it] would not contain a Biblical prohibition but rather only a Rabbinical [prohibition] if he places it there prior to the gentile lighting the fire of the oven as explained in chapter 253 Halacha 27]. Thus here since there are opinions which completely permit [one to place even near an active fire] one may at the very least be lenient regarding placing it there before the oven is lit.
Doing it through a gentile, and not in front of an ignoramus: Nevertheless one should not be lenient in front of an uneducated Jew, and one should do so through a gentile.
Summary-Placing congealed fat in an area where it will melt:
In all scenarios below it is forbidden due to the cooking restrictions to place the item in an area where it can reach Yad Soledes.
If only a minute amount of the melted substance is recognizable outside of the solid food, such as the fat of meat, and certainly if it is completely absorbed within the solid food and is not individually recognizable at all, it is permitted.
If however there is a lot of recognizable melted substance flowing out of the food then initially, if there is no pressing need to do so, it may not be heated even below Yad Soledes, even in direct sun light. However in times of need it may be heated to below Yad Soledes. As well as it may be placed by a gentile, not in the presence of an ignoramus Jew, on top of a heating surface that will eventually be turned on by a gentile.
In any event, Bedieved that one went head and melted it to below Yad Soledes without the above allowances it is nevertheless permitted to be eaten on Shabbos.
One may place butter or margarine onto hot lentils and rice and the like of foods that will absorb the melted butter, if it will not reach the point of Yad Soledes.
One may not place margarine, or fat onto a hot piece of meat [or potato] if it will not reach Yad Soledes.
May one melt congealed chicken, meat or fish gravy near a flame or in the sun?
It may never be melted in an area which will reach Yad Soledes. If it will not be able to reach Yad Soledes then if there will be a nice amount of melted liquid which is apparent, it is forbidden. If however it will become absorbed into the food and thus not be very evident, it is permitted.
However there are Poskim which permit melting gravy of meat, chicken, and fish due to that today people are accustomed to eat them even when congealed, and it thus no longer contains a Nolad prohibition.
May one melt ice cream on Shabbos?
Yes, as ice cream is considered like a food and not like a liquid and thus does not contain a Nolad prohibition.
B. Placing plain ice in an area where it will melt on its own:
Note: The two opinions below as well as the final ruling follows the same opinions and ruling of the previous case of melting fat. Here it is brought in reference to melting ice.
First Opinion: It is permitted to place them in the sun or opposite a bonfire in an area where it cannot become hot to the point of Yad Soledes, and they dissolve there on their own.
Other Opinions: [However] there are opinions which say that [the Sages] only permitted to place [the ice] into a cup [of liquid] being that the dissolved water [from the ice] is not recognizable on its own and is rather mixed into the wine or water that is in the cup. However when the dissolved liquid is recognizable on its own then it is forbidden [to drink this water] even if it already melted, due to the reason explained in Halacha 3A.
The Final Ruling: It was already explained in the previous Halacha that the main Halachic opinion is like the first opinion [here] although that the custom is to initially be stringent [to not melt the ice by placing it near a source of heat, unless it is a time of need. As well it may be done by a gentile not in the presence of an ignoramus on top of a heating surface which he will eventually turn on].
Summary-Placing ice in an area where it will melt on its own:
In all scenarios below it is forbidden due to the cooking restrictions to place the item in an area where it can reach Yad Soledes.
May only be done: a) in times of need, or b) through a gentile, not in the presence of an ignoramus Jew, on top of a heating surface that will eventually be turned on by a gentile.
In any event, Bedieved that one went ahead and melted it to below Yad Soledes without the above allowances it is nevertheless permitted to drink on Shabbos.
May one melt a frozen baby bottle in the sun or near heat in an area that it will not reach Yad Soledes?
May one place ice cubes on top of bottles of soda and the like in order to cool them down?
Yes, as the resultant water will anyways go to waste. It is thus similar to breaking off a piece of ice which is allowed due to that the melted water which is resulted from the breaking goes to waste, as explained in Halacha 1D.
May one throw out his leftover ice cubes into the kitchen sink despite the fact that they will melt?
Yes, as the resultant water is going to waste.
May one place ice cubes in his cup with the intent of having it melt and then drink its water?
May one defrost frozen foods/liquids on Shabbos, such as defrosting a frozen bottle of soda?
Food/liquids that are not eaten in their frozen state: Such as cooked meat [as raw meat is Muktzah], bread, and milk may be defrosted in order to use on Shabbos [as opposed to after Shabbos being that it is forbidden to do any preparations on Shabbos for after Shabbos.]
Foods that are also eaten in their frozen state: May not be defrosted. Thus water/soda/juices which have frozen may not be defrosted on Shabbos due to Nolad, [unless in a case of need, as explained in the summary above]. However there are Poskim which permit to defrost all items, including frozen bottles so long as one does not place it near the sun or fire. [Seemingly according to Admur one is to be stringent].
May one place ice cubes in a serving tray for the meal despite the fact that they will melt?
Yes as one has no intent to drink the melted water but rather only to use the ice and it is thus similar to throwing ice in ones sink which is allowed due to that the liquid will be going to waste.
 Based on Chapter 318. See “The Laws of Cooking” Halacha 8 for the full discussion on this topic.
 Based on a 318/25-27. So rules Rav Farkash in Shabbos Kehalacha 4/14 without bringing any lenient opinion.
 Bris Olam 71; SSH”K 1/38 in name of Rav SZ”A; Az Nidbaru 3/8
 SSH”K 10/7
 There it is explained that the flow of fat is similar to the flow of juice from olives on Shabbos which is forbidden.
 Based on 320/16 and Chapter 318 Halacha 27
 So is implied from Admur above. However in SSH”K 10/3 he writes in the name of Rav SZ”A that ice is different than fat and one should try to initially be stringent to avoid using the liquid even Bedieved. This however clearly does not seem to be the opinion of Admur, being that he equates the final ruling by melted ice to that of melted fat of which one need only initially be stringent.
 Shabbos Kehalacha Vol. 1 p. 212
 Although Admur rules that one is to be stringent due to Nolad, nevertheless since the needs of a child are considered a great need, therefore when there is need to do so it is allowed.
 SSH”K 10/1
 Vetzaruch Iyun as there Admur mentions three reasons why it is allowed and perhaps the reason of that it goes to waste it itself not enough. However in the parentheses when explaining why it is not similar to squeezing fruits Admur only mentions the reason that it goes to waste. Vetzaruch Iyun.
 SSH”K 10/1
 SSH”K 10/3; 1/74 as is the simple implication in Shulchan Aruch 320/16
 As rules Admur in 320/16 that in times of need one may be lenient to follow the opinion which permits doing so.
 See next Q&A
 SSH”K 10/5 in name of Rav SZ”A
 Meat and bread are not Nolad being that their state has never changed. Furthermore milk and other foods which are not eaten in their frozen state are also not considered Nolad as since they are not eaten in their frozen state they are considered by people as liquids as opposed to solids even when they are frozen, and it is thus not considered a new change. [Rav SZ”A ibid footnote 15]
 SSH”K ibid, as is the simple Halacha ruled by Admur that one may not cause frozen water to melt. [320/16] Rav SZ”A as brought in Mioreiy Hashabbos. As well Rav Farkash in Shabbos Kehalacha 2 p. 164 regarding Borer seems to also imply he learns this way as he emphasizes removing bottles from the fridge and not from the freezer even though the cases there are mainly dealing with removing items from ones freezer.
 Sheivet Halevy 7/40; Az Nidbaru 10/10; Tzitz Eliezer 6/34-30;
The Sheivet Halevy differentiates between placing something by a fire and the like or by room temperature saying that only when doing an actual action of placing it by a fire or room temperature is melting forbidden even in accordance to the stringent opinion. Vetzaruch Iyun why placing it near the sun or fire is any more of an action then removing it from a colder climate [the freezer] to a warmer climate [ones room]. Furthermore he brings there a proof for this differentiation from the Halacha that one may place fat near an oven which will be turned on by a gentile, thus showing that only when the Jew does an action is it problematic. Vetzaruch Iyun on this as well being that in that case the Jews action could never make it melt, while here bringing it room temperature is itself enough to make it melt, the same way placing it near a fire is enough to make it melt.
 As according to the opinion which holds that the melting prohibition is due to that it is similar to the flow of juice, based on this there should be no differentiation whether it is defrosted near a flame or on its own.
 Piskeiy Teshuvos 320 footnote 22
 If however one does plan to use the melted water then this is dependent on the above mentioned dispute in the previous two questions. In any event even in such a case, according to all one may first place water in the bowl and then place the ice cubes in it.