Renormalizability of Hot Classical Field Theory

I discuss the possibility of using classical field theory to approximate hot, realtime quantum field theory. I calculate, in a scalar theory, the classical two point and four point function in perturbation theory. The counterterms needed to make the classical correlation functions finite are dictated by the superrenormalizability of the static theory. The classical expressions approximate the quantum ones, when the classical parameters are chosen according to the dimensional reduction matching rules. I end with an outlook to gauge theories.