Heating and Cooling

The rate of heating/cooling depends upon the heat mechanisms operating and numerous factors related to the object itself and the surrounding it interacts with so are you sure?Perhaps you could be more specific.

 

Lets use your example as a thought experiment.Let the two objects have different starting temperatures but apart from that be identical in all respects.Let them be in some sort of thermal contact but completely isolated from the surroundings.If the heat lost by the hot object is gained by the cold object(in other words heating one and cooling the other)then after two minutes the temperature loss of the hot object would equal the temperature gain of the cold object.The situation in real experiments will be far more complex and the outcome depends on several variables.It can make the brain ache just to think about it