Using only global symmetries of QCD, we set up an effective model of quarks at finite temperature near the cross over, including all possible terms up to dimension 6. We first treat this in mean field theory. Then we investigate low-energy fluctuations around it up to one-loop order in fermions below the cross over. Static correlation functions of pions and the cross over temperature, both measured on the lattice, completely suffice to fix all parameters of the theory. We examine predictions of this theory, including those for thermodynamic quantities. The results are encouraging.

14 pages, 6 figures