Keli Sheiyni-Insulating on Shabbos a hot food which has been transferred to a second pot:^[1]

If one removed the food from its original pot and placed it into a second pot, then it is permitted to insulate the second pot.[2]

If one poured the food back into its original pot:^[3] Furthermore even if one goes back and returns the food into the original pot, it is permitted to insulate it.

Materials that add heat: The above allowance only applies to using insulation material that does not add heat, however material which adds heat, is forbidden to insulate with, even completely cold food, and even before Shabbos.

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[1] Admur 257:9“It was only made forbidden to insulate on Shabbos with material that does not add heat, when one is insulating the actual pot in which the food was cooked in, as then the decree that one may come to heat it up is applicable. However, if one removed the food into another pot, it is permitted to insulate it.”; Michaber 257:5; See Piskeiy Teshuvos 257:9

[2] The reason: As the food has already cooled off a little in the walls of the second pot, and the Sages only forbade insulating if the food is [still] hot in the original pot that it was cooked in. [Admur ibid]

[3] Admur ibid “even if one goes back and returns the food into the original pot, it is permitted to insulate it (being that the food has already cooled off a little in the walls of the second pot, and the Sages only forbade insulating if the food is [still] hot in the original pot that it was cooked in.)”; M”A 257; M”B 257:28

^[4] Shabbos Kehalacha Vol. 2 page 52; Piskeiy Teshuvos 257:9; Migdanos Eliyahu 1:83; Chut Hashani 257:6

[5] The reason: As even according to those Poskim that are stringent by a Davra Gush, nevertheless he has performed which cools off the food and hence there is no longer a worry that he may forget that it is Shabbos due to his desire to heat up the food.

^[6] Kuntrus Achron 257:1 “Even if it does not cool it off”; Peri Megadim 257 M”Z 5 in opinion of Rambam; Givas Levona 25; Keren Ledavid 1:77; Zekan Ahron 2:14; Darkei Chaim Veshalom 421; Ketzos Hashulchan 71 footnote 36; Chelkas Yaakov 84; Or Letziyon 2:17-11; Igros Moshe 1:95; Betzeil Hachochmah 2:74; Beir Moshe 1:12; Minchas Shlomo 2:8; Tzitz Eliezer 11:29; Chazon Ish 37:32; Even Yisrael 9:8; Shabbos Kehalacha Vol. 2 page 66; Piskeiy Teshuvos 257:9

Other Poskim: Some Poskim are stringent based on the opinion of Rashi that requires cooling down, to prohibit the use of a thermos being that one does not intend to cool off the water. [Levushei Mordechai 2:55; Tzafnas Paneiach 2:27; Melamed Lehoil 1:45; Shevet Halevi 1:93] Even one who desires to be stringent can simply avoid filling the water until the top [Pnei Shabbos in name of Divrei Yatziv] or through pouring the water into a Keli Sheiyni and then into the thermos. [Levushei Mordechai ibid].

[7] The reason: A the thermos is considered a Keli Sheiyni, and the Sages did not decree against it even if it does not cool off the food. [Igros Moshe ibid based on Rambam] Furthermore, doing so is permitted even according to Rashi that requires cooling down, as the entire prohibition is in covering the thermos, and it is permitted to cover it just like it is permitted to cover any vessel. [See Igros Moshe ibid; Chazon Ish ibid that there is never a prohibition in pouring from one vessel to another even if it insulates]

[8] Piskeiy Teshuvos 257:9

[9] Piskeiy Teshuvos 257:9; Shabbos Kehalacha 11 footnote 68

[10] P”M 257 M”Z 5; Implication of Admur 257:9 “And the Sages only prohibited in the Keli Rishon that it was cooked in”. See Shabbos Kehalacha 11 footnote 68

[11] Chazon Ish 37:32; Piskeiy Teshuvos 257:6

[12] The reason: As there is no prohibition of Hatmana in pouring from one vessel to another even if it insulates, and the entire prohibition of Hatmana is to take insulating material and wrap it around the vessel.

[13] Piskeiy Teshuvos 257:9