  Models incorporating moderately heavy dark matter (DM) typically need charged
(scalar) fields to establish admissible relic densities. Since the DM freezes
out at an early epoch, thermal corrections to the cross sections can be
important. In a companion paper [arXiv:1812.04247v2] we established that the
infrared (IR) divergences accruing from scalar-photon interactions cancel to
all orders in perturbation theory. The corresponding infrared finiteness of
thermal fermionic QED has already been established. Here, we study the IR
behaviour at finite temperatures, of a theory of dark matter interacting with
charged scalars and fermions, which potentially contains both both linear and
sub-leading logarithmic divergences. We prove that the theory is IR-finite to
all orders with the divergences cancelling when both absorption and emission of
photons from and into the heat bath are taken into account. While 4-point
interaction terms are known to be IR finite, their inclusion leads to a neat
exponentiation. The calculation follows closely the technique used for the
scalar finite temperature theory.
