  We derive an exact quantum equation of motion for the photon Wigner operator
in non-commutative QED, which is gauge covariant. In the classical
approximation, this reduces to a simple transport equation which describes the
hard thermal effects in this theory. As an example of the effectiveness of this
method we show that, to leading order, this equation generates in a direct way
the Green amplitudes calculated perturbatively in quantum field theory at high
temperature.
