If heat is the measure of how fast the atoms are moving in an object, than isn't there a limit to how hot that object can get as nothing can go as faster than the speed of light. So because the atoms can't vibrate that fast, will there be a limit to how hot the object can get?
Answer
Wikipedia says at above $1.416785\times 10^{32}~\rm{K},$ all theories breakdown. So, that is theoretical limit. In actuality, 7.2 trillion deg F is the highest known temperature, and that is in Large Hadron Collider (LHC) when they smash gold particles together.
In terms of motion of atoms, the limit would be much lower because, the atoms will fly away as gas. Higher temperatures can be achieved by containing the atoms from flying by compressing them at high pressures. At some point, the compressor will also blast, or evaporate.
One way it can reach very high temperatures is where the heated matter also provides its own compression. That can happen when gravity itself creates compression, so that there is no problem of blast, or evaporation. May be temperatures at the time of big bang, or that of a singularity.
However, the main problem would be that of measuring such temperatures, so, the temperature would be limited by range of the measuring mechanism.
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