The Mitzvah to eat hot food on Shabbos:
It’s a Mitzvah to insulate food for Shabbos in order so one can eat hot food on Shabbos, as [eating hot food] is [part of the mitzvah] of honoring and having enjoyment on Shabbos. [See Q&A]
The law by one who hot food is unhealthy for him: However for one whom eating hot food causes him damage, it is permitted for him to eat [only] cold foods. However one who does not believe in the words of the Sages and prohibits eating hot food on Shabbos, we suspect that perhaps he is a heretic.
It is a Mitzvah to insulate food on Erev Shabbos in the permitted ways to be explained so one can eat hot food on Shabbos
Must one specifically insulate his food, or is may he leave it on the fire from Erev Shabbos?
The main point is that the food stay hot for Shabbos. Thus it makes no difference if one achieves this through insulation or through leaving it over a flame.
Insulating food on Erev Yom Kippur so it will be ready to eat after the leave of Yom Kippur:
First Opinion: There are those that say that insulating on Erev Yom Kippur for after Yom Kippur is forbidden being that it’s considered that Yom Kippur is preparing for a weekday, which is forbidden to be done, and insulation was only allowed to be done in honor of Shabbos.
Other Opinions: However others hold that only if one does an action on Yom Kippur to cause it to prepare for a weekday is it forbidden, however if it occurs on its own then there is no prohibition.
Final Ruling: Although we rule like this latter opinion, nevertheless the custom is to be stringent like the former opinion.
Not to insulate with materials that increase heat:
A. The prohibition; its reasoning and if it applies by cooked foods:
Not to insulate with materials that increase heat: One which desires to remove a pot from on top of a Kirah and insulate it in order so it not become cold, it is forbidden for him to insulate it in a material which increases heat, even if one wants to do so from before Shabbos.
May one insulate with a heating material, food which further cooking will cause damage to? Initially it is forbidden to [insulate with material that increases heat] even if further cooking of this food causes it to condense in a way that is detrimental to it.
The reason for this restriction is because: it is a decree made due to that [if this were to be permitted] one may come to insulate the pot in ember, which is ashes which has coals mixed into it, and then afterwards on Shabbos one [may] forget and stoke the coals.
The reason for why it is allowed to leave half cooked food over a fire from before Shabbos, but is not allowed to insulate a food with a material that increases heat: [The above scenario of insulation] is not similar to leaving a pot on a flame over Shabbos, which is permitted to be done when left on top of a Kirah that is not swept or covered, as long as the food has been cooked to the point of the food of Ben Drusaiy from before Shabbos, as usually insulation is done for the need of [food which will be eaten] the next day. As one insulates the food and covers it so it not cool down by the next day, and therefore it requires to be stoked more [than food left on a flame], in order so the food not cool off over the entire night. However by leaving food on a flame, usually this is done for the [food to be eaten by the] night meal, as one leaves the pot there without insulation, it therefore does not need that much to be stoked if the food has already cooked to the point of the food of Ben Drusaiy from before Shabbos. [Furthermore] even if one were to leave this food [on the flame until] tomorrow, there is [still] no suspicion that one will come to stoke the coals, as the little bit of stoking that can be done will not be of help for it to stay hot until the next day being that the pot is not insulated. However when the pot is insulated, a little bit of stoking can help [it retain heat until the next day] and therefore we are worried that one may come to stoke the coals if the pot is insulated in ember. [Now although the above suspicion only applies to ember, being that it can be stoked, as opposed to other materials which add heat, nevertheless] the [Sages] decreed [against using] any material that increases heat because of [the suspicion involved with] ember. [Furthermore this prohibition applies] even if one insulates [the pot] for the need of the night [meal], being that the Sages did not differentiate in their decree.
Other Opinions by foods cooked to the point of Ben Drusaiy: [However] there are opinions which argue on this and say that even to insulate from before Shabbos in materials which add heat is permitted as long as the food has cooked to the point of the food of Ben Drusaiy [from before Shabbos] just as it is permitted to leave it on a Kirah which is not swept or covered, as explained in chapter 253.
The Final Ruling: In a community that it is the custom to be lenient like this [latter] opinion, one should not protest against them doing so. However this custom should not be followed in other places.
Insulation which does not add heat:
Before Shabbos one may insulate with any material that does not add heat to the food.
Insulation which adds heat:
Before Shabbos it is forbidden to use materials which add heat as insulation.
B. Insulating completely raw meat right before Shabbos begins:
Based on the above reason it is forbidden to insulate even completely raw meat close to Shabbos, as even though it is allowed to leave it [over a fire] being that one will [anyways] not think about it until the next day, [and there is thus no suspicion that one may come to stoke the coals at night, and even the next day there is no suspicion] as the meat is able to [become fully] cooked throughout the entire night without stoking. Now [even if] the meat will be able to cool off afterwards [nevertheless there is no worry that one may come to stoke the coals to prevent this as] a little stoking will anyways not be effective [to keep it warm for the next day] since the meat is not insulated. However when the meat is insulated, we are worried that perhaps one will stoke it after it is cooked in order to retain its heat, so that it not cool down, and for such a purpose [even] a little bit of stoking is effective.
Other Opinions: [However] there are opinions which argue on this and say that even to insulate from before Shabbos in materials which add heat is permitted as long as the food has cooked to the point of the food of Ben Drusaiy [from before Shabbos] or if [the meat] is completely raw literally right before Shabbos, just as it is permitted to leave it on a Kirah which is not swept or covered, as explained in chapter 253.
The Final Ruling: In a community that it is the custom to be lenient like this [latter] opinion, one is not to protests against them doing so. However this custom should not be followed in other places.
Summary- Insulating completely raw meat right before Shabbos begins:
It is forbidden to insulate using material which adds heat even a completely raw piece of meat that was placed in right before Shabbos. Nevertheless, those which are accustomed to be lenient in such a case are not to be protested as they have upon whom to rely.
C. Insulating before Shabbos foods which one does not plan to eat until Shabbos day:
There are those which are even furthermore lenient that even if the food is not completely raw close to Shabbos, nevertheless, if one removes his mind from it until the next day [meaning he does not plan to eat it until Shabbos day], it is considered as if it is completely raw. It is thus permitted to insulate it before Shabbos [even with material that adds heat] for the use of the next day even though it has not yet reached the point of Ben Drusaiy [from before Shabbos].
The Final Ruling: One may not [initially] rely on this opinion, unless it is already after the fact [in which case one may rely on them] as long as this does not occur on a regular basis. [See Q&A]
Summary- Insulating foods before Shabbos which one does not plan to eat until Shabbos day:
It is forbidden to insulate using material which add heat even a food which one only plans to eat the next day. Nevertheless, if one transgressed and insulated such a food with material that adds heat, it may be eaten so long as it is not done on a regular basis.
How many times is considered to be a regular basis?
This needs further analysis. Although we do find by Eiruv Tavshilin, and by the laws of Shechitah that if one had already done so one time in the past, then the second time it occurs he is considered negligent and is treated stringently. However it requires further proof to apply that definition towards here as well.
 As the apostate Tzedoki clan which did not believe in the Oral Torah held that one may never eat hot food on Shabbos. Thus we suspect that one who follows this is part of this clan of heresy.
 Shabbos Kehalacha Vol. 2 page 1
 What honor of Shabbos is there to allow insulating food on Erev Shabbos for after Shabbos? Perhaps it is referring to insulating food on Erev Shabbos for Shabbos, and since the sages allowed one to insulate for Shabbos they did not want to differentiate and thus also allowed insulating for after Shabbos.
 The reason for this is explained in the Mahadurah Basra to be that a person would rather have his food be hot and condensed even in a damaging way, then to be not condensed but cold, and thus the same suspicion applies here too.
 Embers are the glowing, hot coals made of greatly heated  Back then, before gas ovens, fuel had to be constantly added by hand in order for the flame to continue. Thus being that on Shabbos no more fuel may be added, one is only left with whatever amount of fuel was placed before Shabbos. Thus food which is needed for the next day’s meal will usually be insulated, as otherwise, even if left on the fire from before Shabbos it will become cold by the next day. However food needed for the night meal will retain heat without needing insulation. Thus the Alter Rebbe is explaining that being that the laws of Shehiyah only refer to leaving a non-insulated food on top of the fire, therefore it can be assumed that the food is needed for the night meal.
 Meaning that although based on the above explanation the suspicion only applies when one insulates with ember food to be eaten the next day, nevertheless insulating for the night is also prohibited, as once the sages decreed against insulation with materials that add heat, they made the decree inclusive to all scenarios, even those which technically do not have reason to be decreed against.
 Meaning even though that after it has fully cooked throughout the night, since it may cool down by the time the day meal arrives, there is thus room to suspect that one will come to stoke the coals so the food stay warm. Thus the Alter Rebbe explains that we do not suspect for this being that stoking will not help at all in this regard if the meat is not insulated.
 Regarding if this ruling includes also the previous mentioned cases of if the food was completely raw and the like, see Q&A 4 and the footnotes there.
 Meaning that if he has already insulated food for Shabbos day in material which adds heat, then one may be lenient to eat this food on Shabbos. To note that according to the Michaber all the above is forbidden even after the fact.
 Shabbos Kehalacha Vol. 2 pages 11