Ambiguities of the CPT-even aether-like Lorentz-breaking term at the   finite temperature
  In this paper, we consider the finite temperature behaviour of the CPT-even aether-like Lorentz-breaking term in the extended Lorentz-breaking QED and demonstrate that its ambiguities whose presence has been shown earlier in the zero temperature case stay also at the finite temperature. 
T. Mariz, J. R. Nascimento, A. Yu. Petrov, W. Serafim
hep-th