  The temperature dependence of the anomalous sector of the effective action of
fermions coupled to external gauge and pseudo-scalar fields is computed at
leading order in an expansion in the number of Lorentz indices in two and four
dimensions. The calculation preserves chiral symmetry and confirms that a
temperature dependence is compatible with axial anomaly saturation. The result
checks soft-pions theorems at zero temperature as well as recent results in the
literature for the pionic decay amplitude into static photons in the chirally
symmetric phase. The case of chiral fermions is also considered.
