Heat diffusion:

I seem to have pretty good luck when I ask people random physics questions on here, so here goes. I'm working on a problem in Mathematica, and essentially I've got a gel in a thermal bath. I'm raising the temperature on the bath and looking at the heat diffusion in the gel. Since I know nothing about heat diffusion, I'm not sure whether the answer I'm getting makes physical sense. If I keep raising the temperature over say 12 hours and I'm looking at the dispersion of the temperatures over the gel, would it make sense for this dispersion to level off at some (nonzero) number after a couple of hours? That's definitely what I'm getting, but I don't trust my coding at all and I can't rely on physical intuition because I don't really get what's happening. Any insights? Leave a comment or email me, please (kathleen-at-uchicago-edu). Thanks!