  We show how the functional renormalization group can be applied to a study of
chiral symmetry breaking in QCD. We discuss the running gauge coupling at
finite temperature for QCD. For scales smaller than the corresponding
temperature, the coupling is governed by a fixed point of the 3-dimensional
theory. Chiral symmetry breaking is approached if the running coupling drives
the quark sector to criticality. We analyze the phase boundary in the plane of
temperature and number of flavors. For small flavor-numbers, we find good
agreement with lattice results. For flavor numbers near the critical flavor
number, we find that the scaling of the critical temperature is determined by
the zero-temperature IR critical exponent of the running coupling.
