I just learned how to solve this heat problem. I took about 30 min to figure out on paper and about an hour to do it with a mouse. But I'm really happy because we are going to be tested on this tomorrow on this stuff and I'm pretty much rocking it.
This solution is what defines the motion of heat transfer through simple shapes, like squares, or rectangular things. This actually creates a hyperbolic sine (sinh) function. If you watch the play back you'll see where it comes from.
wish me luck