Higher-derivative Lorentz-breaking terms in extended QED at the finite   temperature
  In this paper we discuss finiteness and ambiguities of the higher-derivative Lorentz-breaking terms in extended QED with a magnetic coupling at the finite temperature. We find that, beside of the higher-derivative Carroll-Field-Jackiw-like term and Myers-Pospelov term, many new terms arise in a finite temperature case, but most of them vanish in high temperature limit. 
A. Celeste, T. Mariz, J. R. Nascimento, A. Yu. Petrov
hep-th