What is the actual value of the temperature when I set it = 0?

AFAIK, the temperature is in the denominator, it can’t be 0. So what happened when I set it = 0?

To all intents and purposes the model becomes deterministic, i.e. the responses will be consistent across time. I have seen some slight variation on occasion, this could be due to model tuning or some random element changing very close to flipping token probabilities. In my experience the model acts deterministically.