It seems the history is even more interesting. Supposedly, Fourier wanted to figure out how to keep wine cool, as a Frenchman is wont to do. See section 3 of https://www.tandfonline.com/doi/epdf/10.1080/0020739X.2017.1...
> Joseph Fourier (1768–1830) was attracted by the problem of heat diffusion because he wanted to find the ideal (soil) depth to build his cellar so that the wine remained stored at the perfect temperature in the course of a year. He then attempted to understand how the heat would spread across the surface (for a rich Fourier’s biography, we refer to https://mathshistory.st-andrews.ac.uk/Biographies/Fourier/)
But the biography says nothing about wine or cellars. I think the "wine cellar problem" is a kind of textbook application of his work, but I couldn't find any evidence that this was Fourier's motivating problem.
2/10.