Perturbative calculations of the high temperature ground-state axial v
ector current of fermion fields coupled to gauge fields lead to an app
earance of an additional anomalous Chern-Simons topological mass term
in three-dimensional effective action. In Abelian case contributions c
ome only from the vacuum polarization graph, and in non-Abelian case c
ontributions come from the vacuum polarization graph and the two trian
gle graphs.