Temperature changes the softmax equation[1], not weather or not you are sampling from the softmax result or choosing the highest probability. IBM's documentation corroborates this, saying you need to set do_sample to True in order for the temperature to have any effect, e.g., T changes how we sample, not if we sample [2].
A similar discussion on openai forum also claim that the RNG might be in a different state from run to run, although I am less sure about that [3]
[1] https://pelinbalci.com/2023/10/16/Temperature_parameter.html
[2] https://www.ibm.com/think/topics/llm-temperature#:~:text=The...
[3] https://community.openai.com/t/clarifications-on-setting-tem...