We analyze the consequences of the inclusion of the gluonic Polyakov loop in
chiral quark models at finite temperature. Specifically, the low-energy
effective chiral Lagrangian from two such quark models is computed. The tree
level vacuum energy density, quark condensate, pion decay constant and
Gasser-Leutwyler coefficients are found to acquire a temperature dependence.
This dependence is, however, exponentially small for temperatures below the
mass gap in the full unquenched calculation. The introduction of the Polyakov
loop and its quantum fluctuations is essential to achieve this result and also
the correct large Nc counting for the thermal corrections. We find that new
coefficients are introduced at O(p4) to account for the Lorentz
breaking at finite temperature. As a byproduct, we obtain the effective
Lagrangian which describes the coupling of the Polyakov loop to the Goldstone
bosons.Comment: 16 pages, no figure