> It becomes a dirac-delta function. I.e. in a discrete setting (like for LLMs with a finite set of output tokens), probability P becomes one for argmax and 0 for everything else. Only in coding practice it is easer to implement T=0 as a simple if check that directly chooses argmax instead of calculating the limit of some function that includes 1/T quotients.

I don't understand the distinction you're drawing. A Dirac delta function is a "simple if check".

The point is that the case T=0 doesn't just "exist" as a special code branch - it is still well defined mathematically without any change to the output function. What the above comment refers to with the extra "if" check is just a limitation of computers not liking to divide anything by zero, even if the actual function exists and is well behaved at zero. It is not some weird or special theoretical construction.