Expressive Temperature

one thing is phrased a bit confusing: the statistical weights are supposedly "divided by temperature", but if all probabilities are scaled with some factor and renormalized you end up with the original weight distribution.

the author obviously intends to denote that the weights are similar to the weights in statistical mechanics and proportional to exp(-E/(kT))

In example given any 2 outcomes A and B from the distribution at temperature "1.0" with probability ratio P_A / P_B then at temperature "0.5" the probability ratio of the same 2 outcomes will be the square of the original ratio

Is the temperature semantically different from 'yet another input' into the model? Asking as an ML noob.