Here are the rules :

1. Heat flows from warmer objects to cooler objects
2. Heat can not flow from a cooler object to a warmer object

Therefore, if the temperature of the cooler object increases – the only way to maintain the condition of rule 1 is for the temperature of  warmer object to also increase.

People are making the mistake of not understanding the difference between heat and temperature. The diffusive heat flow between a 30 degree location and a 20 degree location is the same as the diffusive heat flow between a 70 degree location and a 60 degree location.

BTW – I used to model heat flow for a living. Feel free to make a fool of yourself though.