  Lorentz and CPT violating QED with massless fermions at finite temperature is
studied. We show that there is no ambiguity in the induced coefficient of the
Chern-Simons-like term that defines the so-called Carroll-Field-Jackiw model at
high temperature. We also show that this system constitutes an example where
the breaking of CPT and Lorentz symmetries is more severe at high temperature
than in the zero temperature case thus precluding any naive expectations of
Lorentz symmetry restoration.
