>> Small question: The rate at which an object looses heat. Clearly this 
>> is proportional to how much hotter it is than its surroundings. But is 
>> this relationship linear?
> 
> No.  The radiation of energy due to heat is proportional to the fourth 
> power of the absolute temperature.

And how about the conduction and/or convection of heat as a function of 
temparature difference?

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