It is forbidden to insulate hot food on Shabbos – your interest in hot food may tempt you to heat up food that cooled down before insulating it. This prohibition doesn’t apply during bain hashmashos – only when it is undoubtedly Shabbos. (ShA1 – MB1)
On Friday you may insulate hot food for Shabbos only in material that does not add heat, but if the material adds heat you must remove the food from the insulation before dark. (ShA1 – MB6)
The only time you can insulate in material that adds heat is on Friday for the purpose of eating it hot after Shabbos. (MB4)
If you did hatmanna with something that normally adds heat but the food did not become hotter, there is no penalty (that you can’t eat it) since no added benefit came about from the issur. That explains why there is no issur to eat food that was insulated on Shabbos in material that does not add heat – you have no added benefit. (ShA1 – MB8)
If your intention with covering the food with insulating material is merely to keep it safe from mice or clean from dirt, it is allowed. (ShA2)
If you insulated food before Shabbos in pillows, blankets, clothes, saw dust, feathers and the like – material that does not add heat – and it became uncovered on Shabbos, you may return the covering. Not only that, you may even add food inside the insulation and even add material to the insulation. (ShA3,4)
Here are the two cases that you can do hatmanna on Shabbos (as long as the material doesn’t add heat):
Transfer the food out of the kli rishon (then you can put it back in) before insulating.
Insulate the food that cooled down (to less than yad soleddes?) so it should not cool down further. (ShA5,6)
When doing shehiya in the prescribed manner detailed in Siman 253, be sure not to cover the pot with hatmanna material even on erev Shabbos. The hot coals of the kira add heat and are part of the hatmanna. Some poskim allow it when the coals have all been swept out or when the pot is on top of a hot oven. Do not protest against those who want to be maykil. (ShA8 – MB43)
If the hatmanna material is draped over the pot in a way that the material does not touch the sides of the pot – it is permitted. Chazal do not consider it derech hatmanna. (ShA8)
It is a mitzva of kavod and oneg Shabbos to cook hot food and insulate it and to eat it hot on Shabbos (unless it is bad for your health). Whoever forbids eating hot food on Shabbos is suspected to be an apikores. (Rama8 – MB48)
The Baal Hama’or writes you should become fat with oneg Shabbos. (MB49)