Every token from the last page eventually reaches the same moment: a list of candidate next tokens, each with odds attached. Page 3's temperature slider reshapes these bars. It doesn't decide how much of the list the model is even allowed to pick from — that's a different knob, or two.
This is why the same question can get two different answers, and the knob for taming that: turn a cutoff down for safer, more repetitive replies, or up for more variety — and more nonsense.
Nothing excluded yet — every candidate above is still in play, just less or more likely depending on temperature.
A third, unrelated knob
Neither temperature nor a cutoff can do this — a stop sequence just halts the model the moment it appears, mid-thought if necessary.
So what
Temperature reshapes the odds. Top-p and top-k decide which odds you're even allowed to see. Three different knobs, not one.