A. The law if the insulation does not touch the walls of the pot:
If the [pot was insulated] in a way that the clothing are not touching the pot, such as if one placed over the pot of food a wider pot which [is wide enough that it] does not touch the sides of the pot [with food] and one then placed the clothing on the [external] pot, in which case it ends up that there is no insulation involved here at all, not even with a material that does not add heat, then it is permitted to be done. [See Q&A]
The reason is: because the Sages only prohibited insulating with material that adds heat because of a decree that [if this were to be allowed] one may come to insulate in embers. Therefore [insulating] is not prohibited unless it is done in a way similar [to insulating with] embers, [meaning that just like embers] is moveable and is attached to the walls of the pot [so too all insulation is only prohibited if it is moveable and attached to the walls of the pot]. [Thus being that] the walls of an oven and its opening are not attached to the pot [therefore it is not prohibited to leave a pot inside from Erev Shabbos]. ([This applies] even if the oven is small and narrow, as it is not possible that there isn’t a little bit of air separating the [walls of the oven from the pot])
The insulating material must touch the actual walls of the pot otherwise it is not defined as insulation, and is allowed to be done even with material that adds heat.
If one insulates around a pot that has handles, and thus by the area of the handles the material is not touching the pot, is this still considered insulation?
According to the Alter Rebbes ruling in the Mahadurha Basra that even insulating the top of a vessel is problematic, would it be prohibited on Shabbos to place a wide pot on top of a pot of hot food and then cover it with a towel, being that the wide pot touches the cover of the pot?
No. This is allowed even according to the Mahadurah Basra.
B. How much of the pot must be insulated for it to be considered a prohibited insulation?
According to the Shulchan Aruch of Admur the ruling is the following: In 453/10 Admur defines insulation as fully covering the entire pot with insulating material. In His words “Even if burning coals surround and are attached to the walls of the pot, [nevertheless] this is not considered [the prohibition of] insulation being that the pot is open from the top, [meaning it has no coals surrounding its top].” Similarly in the Kuntrus Achron here number 3 the Alter Rebbe reiterates and explains this ruling, that only if both the walls and the top [meaning the pot cover] is insulated with material is it considered insulation. This ruling is also repeated here in 457/4 and in the summary of the laws of insulation brought in Chapter 259, at the very end, and is the simple understanding in chapter 253 Halacha 14. [The Sheivet Haleivi rules like this opinion, and does not make mention of the Mahadureah Basra.]
Ruling of Admur Mahadurah Basra: In the Mahadurah Basra for chapter 259 the Alter Rebbe elaborates on the opinions which rule that by insulation which adds heat we do not take the top of the pot into account. Thus possibly even if only majority of the walls are covered, it would be considered insulation. [Seemingly Rav Shlomo Zalman Aurbach also rules like this opinion.] [See footnote for opinion of Michaber and Mishneh Berurah ]
Summary- How much of the pot must be insulated for it to be considered a prohibited insulation?
See above for an elaboration on the different opinions on this. The following is the final ruling as ruled by Rav Farkash in Shabbos Kehalacha.
- By material that adds heat:
Majority of the walls of the pot: One should Lechatchilah consider it to be prohibited insulation even if only majority of the walls of the pot are covered, even if its top is uncovered by the insulation material.
However by a pressing situation, or Bedieved, one may be lenient that as long as the pot is not fully covered by the insulation, such as that one covered only its walls and left its top uncovered [by the insulation, however it may have its pot cover on it], then it is allowed.
Minority of the pot: If only minority of the pot is covered, even if the cover of the pot is covered with insulation, it is allowed even Lechatchilah.
Leaving the bottom of the walls uncovered: Regarding if one may initially insulate the pot in a way that the entire bottom area of the walls are visibly uncovered, then see footnote.
- By materials which do not add heat: This is not relevant to this chapter being that insulating with such material is permitted before Shabbos. See Chapter 2 Halacha 2 with regards to the laws of insulating on Shabbos.
If the food does not fill the entire pot, is it still considered insulated if the majority area of the walls where the food reaches is insulated?
We measure against the pot itself and not against the walls of the pot that correspond to the food. Thus even if the entire area of the food is insulated, but this area is only a minority of the pot, it is even initially allowed to be done.
 Meaning that this type of insulation is not even considered a minor form of insulation, which is insulation with material that does not add heat.
 Thus one may as well place a wide board or metal over the top of the pot and then cover it with clothing, as the clothing do not touch the side of the pot.
 Shabbos Kehalacha Vol. 2 page 5
 Shabbos Kehalacha Vol. 2 page 21
 The proof: This Halacha here is going in continuation of the opinion of the Beis Yosef which holds like the Alter Rebbe in the Mahadurah Basra, and thus if according to him its allowed, then it is allowed also according to the Mahadurah Basra. The reason: It is only problematic when one places material on top of a pot for the purpose of insulation, however when placed for another purpose, as is done here, that the upper pot is being placed in order to intervene between the towel and the lower pot, then it is allowed.
 According to the Michaber the ruling is that by materials that add heat, insulation of any amount is forbidden.
According to the Mishneh Berurah it is unclear whether he holds like the ruling of Admur in the Shulchan Aruch, that it must all be covered to be forbidden, or if he rules like the Kuntrus Achron of Admur that even insulating majority of the walls is not allowed.
 Shabbos Kehalacha Vol. 2 page 14-24
 This is based on the Mahadurah Basra where the Alter Rebbe brings up the possibility that this is the definition of insulation, and thus we rule Lechatchilah to be stringent like this opinion.
 This is based on the ruling in the Shulchan Aruch.
 Rav Shlomo Zalman Aurbach permits this form of insulation, even if majority of the pot is covered by its upper side. However Rav Farkash doubts whether one may initially rely on this ruling being that it has not been brought in any of the previous Poskim.
 Shabbos Kehalacha Vol. 2 page 18