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

Lorentz-violating Chern-Simons action under high temperature in massless QED