Heat is just energy. When you look at physics we were taught it was mass that is the culprit when it comes to the limit of C. Well not really. Mass is actually the bi product. The energy in the system dictates the relative mass. This is why relative mass increases with velocity. The limit you are thinking about is the same limit. The more heat in a confined space will increase the relative mass. Gravity is the symmetrical balance to energy and mass is more like a side product. At some point you will cross the Schwartzchild limit and create a black hole. That is the theoretical limit. As to what humans can produce in a confined space is just an engineering issue.
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