Which of the pots will cool the contents faster? Where is the ice on the lid of the pot or under the pot itself?

If the pan is completely filled to the brim with the contents, and the lid closes it tightly and there is no air gap, then it will cool faster if you put ice on it. The warmer liquid content will cool and sink to the bottom, while the warmer liquid will rise and cool from the ice.

On the other hand, if the pan is not filled to the brim, it is more profitable to put ice under the pan, because cooling through “ice – metal – content” will be more efficient than through “ice = metal – air gap – content”, since the thermal conductivity of the air is very low.