  Recently it has been questioned, notably in the context of the scalar singlet
dark matter model with $m_\varphi^{ }\simeq 60$ GeV, how efficiently kinetic
equilibrium is maintained if freeze-out dynamics is pushed down to low
temperatures by resonant effects. We outline how Langevin simulations can be
employed for addressing the non-equilibrium momentum distribution of
non-relativistic particles in a cosmological background. For a scalar singlet
mass $m_\varphi^{ }\simeq 60$ GeV, these simulations suggest that kinetic
equilibrium is a good approximation down to $T \sim 1$ GeV, with the deviation
first manifesting itself as a red-tilted spectrum. This reduces the
annihilation cross section, confirming findings from other methods that a
somewhat larger ($ < 20\%$) coupling than in equilibrium is needed for
obtaining the correct abundance.
