I assume that there was a single person that at a specific day in time was the first to see and understand perfectly clearly that temperature is somehow identical with the mean kinetic energy of a bunch of molecules or atoms, and who was able to write this done as a mathematical equation.
Even though this idea grew slowly - over generations of physicists and inside the mind of this one physicist - I believe it became clear to him somehow suddenly (accompanied by an eureka effect).
Do we know who this person was, and when it happened (roughly)?
Or do you believe this question doesn't make sense or is unanswerable?