Is it possible to mathematically explain why solids go under mollification when heated? Well, I'm sure that many people on MSE might object that this is not a math question, however, I think that there might be a well-posed mathematical answer to this question, or at least I hope so.
We all have seen in our every day life that if we heat a heat conducting solid it starts to get smoother like in this picture:

Is it possible to mathematically explain why the solid tends to get a smoother shape after it's heated?
I'm asking this question because I found the idea similar to what mollifiers do in distribution theory.

My totally disinformed opinion: when the body starts to melt the relevant forces are surface tension and gravity. Surface tension wants to minimize the surface and kills the edges. Gravity pulls down. I would be surprised if the result could be expressed as a convolution in a natural way.
EDIT: expanding the commeny by Zack Li, in the case of temperature the answer is yes. The temperature is the convolution of initial temperature with the heat kernel/fundamental solution.
