  We settle the ``apparent'' paradox present in thermal QED_3 that the
perturbative series is not invariant, as manifested by the temperature
dependence of the induced Chern-Simons term, by showing that large (unlike
small) transformations and hence their Ward identities, are not perturbative
order-preserving. Instead the thermal effective gauge field actions induced by
charged fermions in QED_3 can be made invariant under both small and large
gauge transformations by suitable regularization of the Dirac operator
determinant, at the usual price of parity anomalies. Our result is illustrated
by a concrete example.
