An effective photon mass and equivalent photon charge are calculated for plasmas with finite temperature, by using a second covariant quantization of the electromagnetic field, which is based on a nonlinear magnetofluid unification field formalism. Relativistic effects are considered both in the fluid bulk motion and in the thermal motion. The effective relativistic photon mass is found for transverse and longitudinal photons, while the equivalent relativistic photon charge is obtained for purely transverse photons. Both quantum quantities are the relativistic generalization, at finite temperature, of previous results [Mendon a et al., Phys. Rev. E 62, 2989 (2000)]. The dependence with temperature is studied in both cases.