QED second order corrections on the speed of light at low temperature

We want to study thermal corrections on the speed of light at low temperature considering temperature dependence of photon vacuum polarization tensor at two-loop level in the standard QED. It is found that the heat bath behaves as a dispersive medium for the propagation of light and reduces its speed proportional to the second order of temperature. Similarities and differences، in light of already known calculations which are based on Euler-Heisenberg Lagrangian and/or those using temperature dependent electromagnetic properties of the medium are discussed.