What is Fourier's Law of Heat Conduction?

An introduction to Fourier's Law of Heat Conduction, in one dimensionHeat conduction is transfer of heat from a warmer to a colder object by direct contact. A famous example is shown in A Christmas Story, where Ralphie dares his friend Flick to lick a frozen flagpole, and the latter subsequently gets his tongue stuck to it. The mathematical model was first formulated by the French physicist Jean Baptiste Joseph Fourier, he of the eponymous Fourier Series. He found that heat flux is proportional to the magnitude of a temperature gradient. His equation is called Fourier's Law.