  Thermal production of light dark matter with sub-GeV scale mass can be
attributed to $3\rightarrow 2$ self-annihilation processes. We consider the
thermal average for annihilation cross sections of dark matter at $3\rightarrow
2$ and general higher-order interactions. A correct thermal average for initial
dark matter particles is important, in particular, for annihilation cross
sections with overall velocity dependence and/or resonance poles. We apply our
general results to benchmark models for SIMP dark matter and discuss the
effects of the resonance pole in determining the relic density.
