  The effective potential of Yang-Mills theory at high temperature derived by
Gross, Pisarski, Yaffe and Weiss is critically reexamined and it is argued that
the groundstate of the potential at <A0>=0 is invalid, due to the infrared
divergence of the Matsubara zero mode. This suggests that the thermal
groundstate is dominated by infrared non-perturbative effects. Lattice
simulations are carried out and the field A0 in the static gauge is observed to
acquire nonzero, non-perturbative expectation values at high temperatures. A
consequence is that thermal perturbation theory is inconsistent with the
non-perturbative groundstate and it cannot account for all of the contributions
to a thermodynamic quantity at any temperature. Related issues, including
dimensional reduction and confinement, are also discussed.
