Question

what is the relationship between the amount of energy passed and the heat produced

Answer 1

Heat!!!!here is your answer.
This method is known as"Principle of method of mixtures"
when two or more bodies at different temperatures are brought into thermal contact, then net heat lost by the hot bodies is equal to net heat gained by the cold bodies until they attain thermal equillibrium.
NET HEAT LOST=NET HEAT GAIN.