  The possibility of a Chern-Simons like term generation in an extended model
of QED, in which a Lorentz and CPT non-covariant interaction term for fermions
is present, has been investigated at finite temperature and in the presence of
a background color magnetic field. To this end, the photon polarization
operator in an external constant axial-vector field has been considered.
One-loop contributions to its antisymmetric component due to fermions in the
linear order of the axial-vector field have been obtained. Moreover, the first
nontrivial correction to the induced CS term due to the presence of a weak
constant homogeneous color magnetic field has been derived.
