Temperature is a spread, not a creativity switch
At temperature zero the model takes the same next word every time. That is what I want when I am pulling a date, a name, or a value that is already in the text. There is nothing to invent, and a second run should not disagree with the first.
Turn the dial up and the choice spreads. Some of the new choices are useful. Some are confident and wrong in a way the low setting would not have been. I stopped calling the high setting creativity. It does not know whether I wanted another wording or whether I wanted the identifier left alone.
If I want another option I ask for another option, and I say what must stay the same. The dial stays low unless I am deliberately willing to throw the answer away.