  In this work we investigate the radiatively induced Chern-Simons-like terms
in four-dimensions at zero and finite temperature. We use the approach of
rationalizing the fermion propagator up to the leading order in the
CPT-violating coupling $b_\mu$. In this approach, we have shown that although
the coefficient of Chern-Simons term can be found unambiguously in different
regularization schemes at zero or finite temperature, it remains undetermined.
We observe a correspondence among results obtained at finite and zero
temperature.
