So, I've taken to running the game in small doses and only when the room is cool, and haven't had any more trouble. Small doses is good anyway, since the game is click-heavy... ESPECIALLY for my hit-and-run assassin. My hand gets tired.
Trying the game on a computer with a vastly superior graphics card? Led to the graphics card going into a panic attack about lack of power and throttling the owner.
Clearly, my antiquated methods are superior.
I'm level 20-something at the moment, in Egypt, with a damage-per-second of around 180-190. I don't know if that's good or not. Of course, considering all the random chances and damage-over-times I have on the character I don't know if that's accurate or not, either. All I can say is that most things die pretty fast.