  Using an approach developed in the context of zero-temperature QCD to
systematically sum higher order effects whose form is fixed by the
renormalization group equation, we sum to all orders the leading log (LL) and
next-to-leading log (NLL) contributions to the thermodynamic free energy in hot
QCD. While the result varies considerably less with changes in the
renormalization scale than does the purely perturbative result, a novel
ambiguity arises which reflects the strong scheme dependence of thermal
perturbation theory.
