  We develop the heat kernel method in the context of finite temperature
quantum field theory. We compute the heat kernel expansion in the presence of
general gauge and scalar fields which may be non Abelian and non stationary.
The Polyakov loop appears at finite temperature as a new gauge covariant
operator. We apply this method in the computation of the fully gauge invariant
effective action of QCD in the regime of high temperature. It is obtained the
dimensionally reduced effective action of QCD as well. In the context of chiral
quark models, in particular the Nambu--Jona-Lasinio and the spectral quark
model, we apply this method to compute the low-energy chiral Lagrangian at
finite temperature. The coupling of the Polyakov loop with these models allows
to solve some inconsistencies appearing in the standard treatment at finite
temperature: generation of multi-quark states, large $N_c$ counting, etc. On
the other hand, we show that recent available lattice data for the renormalized
Polyakov loop above the deconfinement phase transition exhibit unequivocal
inverse power temperature corrections driven by a dimension 2 gluon condensate.
This simple ansatz provides a good overall description of the data throughout
the deconfinement phase until near the critical temperature with just two
parameters. Finally, we study several chiral quark models in the light of
chiral perturbation theory in curved space-time. The low energy structure of
the energy momentum tensor in these models with SU(3) flavor symmetry is
analyzed in the presence of external gravitational fields.
