  The dark matter relic density has been increasingly accurately measured by
successive generations of experiments. The Boltzmann equation determines the
yields using the dark matter annihilation cross section as one of the inputs;
the accurate computation of the latter including thermal contributions thus
assumes importance. We report here the next-to-leading order (NLO) thermal
corrections to the cross sections for (Majorana) dark matter annihilation to
standard model fermions: $\chi \chi \to f \overline{f}$, via charged scalars.
We use a novel approach, utilising the technique of Grammer and Yennie,
extended to thermal field theories, where the cancellation of soft infra-red
divergences occurs naturally. We present the NLO thermal cross sections in full
detail for both the relativistic case as well as in the non-relativistic limit.
Our independent calculation verifies earlier results where the leading
contribution at order ${\cal{O}}(T^2)$ was shown to be proportional to the
square of the fermion mass in the non-relativistic limit, just as at leading
order. We find that the ${\cal{O}}(T^4)$ contributions have the same dependence
on the fermion mass as well.
