  We study the vacuum polarization tensor of QED (quantum electrodynamics) at
high temperatures up to the two loop levels and its effect on the
electromagnetic properties of a medium. One loop corrections to QED coupling
vanish at low temperatures (T$\leq 10^{10}K$), but they play an important role
at high temperature ( T$\geq 10^{10}$ K) to study the behavior of QED medium at
these temperatures. At low temperatures ( $T \leq m_e$)higher order loops give
a tiny correction due to the coupling of radiation with matter and an overlap
of hot photon loop with cold fermion loop contributes to this effect. These
higher loop contributions does not affect the convergence of perturbative
series, and renormalizability of QED is guaranteed at temperatures around
neutrino decoupling. We use the renormalization scheme of QED at finite
temperature in real-time formalism to study the dynamically generated mass of
photon indicating the plasmon production in such a medium. Temperature
dependence of this QED plasma parameters is discussed. We explicitly show that
this behavior of a thermal medium exists upto temperatures of a few MeV only.
We compare the first order and second order effects upto the 4MeV temperature
and demonstrate that the higher order contributions are smaller than the lower
order contributions proving the renormalizability of the theory. The lowest
order contributions are sufficiently smaller than the original value as well.
