QED effective action at finite temperature: Two-loop dominance

We calculate the two-loop effective action of QED for arbitrary constant electromagnetic fields at finite temperature T in the limit of T much smaller than the electron mass. It is shown that in this regime the two-loop contribution always exceeds the influence of the one-loop part due to the thermal excitation of the internal photon. As an application, we study light propagation and photon splitting in the presence of a magnetic background field at low temperature. We furthermore discover a thermally induced contribution to pair production in electric fields.