You would never have such litigation in the first place--there is no such tort or legal concept of "too hot".

On the other hand, if the player were to sue for negligence, then the question of whether it was "too hot" is a factual question that the jury would decide, after the lawyers present evidence for their preferred answer (and possibly evidence against the undesired answer).

The jury's finding would be a finding of "fact" as to whether it was "too hot" would apply only to that case, because their finding would necessarily depend on the specific facts of that case. Juries cannot make findings of "law", which are general principles/rules that can be applied to other cases.

> Would the lawyer define "too hot", or would the jury?

The jury.

> the legal system would treat the jury's definition almost as definitively as a temperature reading input into an algorithm, right?

For this case, yes. For all time, no. The fuzzy set of "too hot" would become the legal precedent (the stare decisis). The actual temperature would remain a question of fact and not law.

If you read up on how fuzzy logic is applied in control systems, you'll see that there's always steps to take non-fuzzy inputs and "fuzzify" them before performing the fuzzy logic itself. Afterwards you de-fuzzify to get a crisp output.

Courts work very much like that: the law retains fuzziness because no crisply algorithmic system can encompass the total complexity of the human world. That's how equity arose ... which is a law history lesson for another day.