Okay, something just tweaked in my brain. Do higher temperatures essentially unlock additional paths for a model to go down when solving a particular problem? Therefore, for some particularly tricky problems, you could perform many evaluations at a high temperature in hopes that the model happens to take the correct approach in one of those evaluations.

Edit: What seems to break is how high temperature /continuously/ acts to make the model's output less stable. It seems like it could be useful to use a high temperature until it's evident the model has started a new approach, and then start sampling at a lower temperature from there.