  For a large class of field theories there exist portions of parameter space
for which the loop expansion predicts increased symmetry breaking at high
temperature. Even though this behavior would clearly have far reaching
implications for cosmology such theories have not been fully investigated in
the literature. This is at least partially due to the counter intuitive nature
of the result, which has led to speculations that it is merely an artifact of
perturbation theory. To address this issue we study the simplest model
displaying high temperature symmetry breaking using a Wilson renormalization
group approach. We find that although the critical temperature is not reliably
estimated by the loop expansion the total volume of parameter space which leads
to the inverse phase structure is not significantly different from the
perturbative prediction. We also investigate the temperature dependence of the
coupling constants and find that they run approximately according to their
one-loop $\beta$-functions at high temperature. Thus, in particular, the
quartic coupling of $phi^4$ theory is shown to increase with temperature, in
contrast to the behavior obtained in some previous studies.
