I personally think it's not going to be incredibly difficult. Obviously, the way it was done with QuietSTaR is somewhat expensive, but I see many reasonable approaches here that could be considered.

High temperature will obviously lead to randomness, that's what it, evening out the probabilities of the possibilities for the next token. So obviously a high temperature will make them 'crazy' and low temperature will lead to deterministic output. People have come up with lots of ideas about sampling, but this isn't really an instability of transformer models.

It's a problem with any model outputing probabilities for different alternative tokens.