Since heat is defined as the movement of molecules, and because of relativity time slows for faster moving objects, would a hot object be in a slower time frame then a cooler object, because the hot objects molecules are moving faster?
Answer
No, the hot object itself experiences no relativistic effects. The particles in the object however may well experience time dilation or length contraction. In fact in very hot gases and plasma, ideal gas laws may not always apply due to relativistic effects.
These effects are especially noticeable in gases once the kinetic energy or fermi energy (for fermionic gases) exceeds $mc^2$ by a significant amount.
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