[yorwba]

The Wikipedia article on the heat equation has a section on using Fourier series: https://en.wikipedia.org/wiki/Heat_equation#Solving_the_heat...

I assume that except for the adaptation to modern notation, the general idea of the argument has been preserved.

Note that sinusoids are only used because they make the calculations convenient, and not because of the day/night cycle or actual sinusoidal heat distributions empirically observed in nature.