Abstract
The total perturbative contribution to the free energy of hot $\mathrm{SU}(3)$ gauge theory is argued to lie significantly higher than the full result obtained by lattice simulations. This then suggests the existence of large nonperturbative corrections even at temperatures a few times above the critical temperature. Some speculations are then made on the nature and origin of the nonperturbative corrections. The analysis is then carried out for quantum chromodynamics, ${SU(N}_{c})$ gauge theories, and quantum electrodynamics, leading to a conjecture and one more speculation.
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