  We study the discrete and gauge symmetries of Quantum Electrodynamics at
finite temperature within the real-time formalism.
  The gauge invariance of the complete generating functional leads to the
finite temperature Ward identities. These Ward identities relate the eight
vertex functions to the elements of the self-energy matrix. Combining the
relations obtained from the $Z_2$ and the gauge symmetries of the theory we
find that only one out of eight longitudinal vertex functions is independent.
As a consequence of the Ward identities it is shown that some elements of the
vertex function are singular when the photon momentum goes to zero.
