Newton's law of cooling, a staple of the Calculus curriculum, is an empirical law not meant for mathematical proof. However, we show it is mathematically equivalent to the intuitively appealing principle that the average temperature of two cooling objects is equal to the temperature of a single object with initial temperature the average of the other two.
Northshield, S. (2007). Not mixing is just as cool. Mathematics Magazine, 80 (4), 294-298.