  Previous calculations of the thermal beta-function in a hot Yang--Mills gas
at the one--loop level have exposed problems with the gauge dependence and with
the sign, which is opposite to what one would expect for asymptotic freedom. We
show that inclusion of higher--loop effects through a static Braaten--Pisarski
resummation is necessary to consistently obtain the leading term, but alters
the results only quantitatively. The sign, in particular, remains the same. We
also explore, by a crude parameterization, the effects a (non--perturbative)
magnetic mass may have on these results.
