I the food is completely cooked it permitted to put the cover ant towel back one top. However, if there patrts which aren’t fully cooked , even if there is doubt it is forbidden to put it back on Shabbat.
Explanation:
The Mishna in Shabbat (51a) says: If he did not cover it the day before eh y not cover it on Shabbat. If he did and it came off it is permitted to cover it.
The Gemara quotes a Beraita: The Rabbis Taught even though we say it is forbidden to insulate food even either things which don’t add heat after dark, he may add to it. How? Rabban Shimon ben Gamliel says you take off the cloth and put on Glufkorren (Rashi explains it as jacket which retains more heat then cloths.) Or take off the jacket and upon cloths.
The Mishna says that a food which became uncovered it is permitted to cover it. It does not say when it became uncovered on Erev Shabbat not on Shabbat. Nor dos itsy if happened by itself or someone did it. The Rishonim argue:
Tosfot (Shabbat 51a) says when the Mishna allows to recover it is not only if been uncovered by itself even if it was uncovered by a person he may not late it .whet he Mishna says , “He covered it and it became uncovered,” is referring to Ere Shabbat if it became uncovered. so only permitted to recover on Shabbat if it became uncovered by itself but if it was uncovered by a person in order to recover it on Shabbat that is Hatmanah and forbidden.
The Rosh writes the words “it was covered and became uncovered,” which seems it happened by itself is only if it happened before sundown. If he uncovered without intent to recover it on Shabbat it is forbidden to cover it on Shabbat. The Korban Netanel understood the Rosh argues with Tosfot. Tosfot writes if he uncovered it on Erev Shabbat to cover it after sundown, it is forbidden to cover it. The Rosh says it is forbidden to cover pots after Shkiah if he uncovered it on Erev Shabbat he did not intend to recover it on Shabbat then it is forbidden to cover it on Shabbat, but if he had intent to recover it is fine.
The Bach says it’s a mistake and the Rosh and Tosfot are the same.
The Rambam writes Chamin which was insulated on Erev Shabbat and came uncovered on Shabbat is permitted to cooer. He understands only if it became uncovered but if someone purposefully uncovered it, no. Only if it became uncovered on Shabbat but if became uncovered on Erev Shabbat, no.
So rules the Shulchan Aruch (OH 257:4)
It is point to point out there is no problem of Hatamanah when you cover the cover of the pot and don’t wrap it around the pot, as the Rema says in 253:1. Even though the Shulchan Aruch argues that even if it’s left t uncovered on the sides if it is on coals it is Hatmanah, that tis only coals but a hot plate which one can’t stick it inside and even more the fire is not directly under the pot. That is not considered Hatmanah. Therefore, there should not be any problem of Hatmanah on the pot cover on the hot palette according to everyone.
However, we must be sure to be careful if we put the cover back the food is completely cooked. Sometimes we add some rice or beans right before Shabbat and it will not be cooked yet. It forbidden to cover things which are not cooked fully since it cooks it after. Even if there is a doubt if the food is completely cooked it is possible Torah transgression.