What is the simplest effective approach to hot QCD thermodynamics?

The dimensionally reduced action is believed to provide for a theoretically consistent and numerically precise effective description of the thermodynamics of the quark-gluon plasma, once the temperature is above a few hundred MeV. Although dramatically simpler than the original QCD it is, however, still a strongly interacting, confining theory. In this talk I speculate on whether there could exist a further simplified recipe within that theory, for physically relevant temperatures, which would already lead to a phenomenologically satisfactory description of the free energy and various correlation lengths of hot QCD, but with only a minimal amount of numerical non-perturbative input needed.