  In this work we apply the Matsubara-Fradkin formalism and the Nakanishi's
auxiliary field method to the quantization of the Podolsky electrodynamics in
thermodynamic equilibrium. This approach allows us to write consistently the
path integral representation for the partition function of gauge theories in a
simple manner. Furthermore, we find the Dyson-Schwinger-Fradkin equations and
the Ward-Fradkin-Takahashi identities for the Podolsky theory. We also write
the most general form for the polarization tensor in thermodynamic equilibrium.
