Call the temperature of the universe at quark confinement (light/matter separation - an observable event, perhaps the earliest possible observable event) Tmax. So you have a scale from 0 to Tmax.
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Even if you do man an argument to an upper limit on temperature it is missing the point of the question... we are talking about representing a single-bounded variable with a double bounded range lineraly... that isnt possible. Arguing that temperature is in reality double bounded, while true, was not the point of the question.
I guessed that without going back to read the full argument. However, you did pose a challenge, and I took a shot at it.
