Cancellation of mass singularities in thermal reaction rates

Thermal amplitudes exhibit mass singularities when particle(s) with vanishing mass is (are) involved. We show that such singularities do not appear in the perturbation expansions of the thermal reaction rates, provided the theory in consideration does not bring about such mass singularities in zero-temperature reaction rates. The latter is supposed to be the case for physically sensible quantities in a wide class of theories, including QED and QCD (Kinoshita-Lee-Nauenberg theorem).