For a quantitative investigation on the time evolution of heavy thermal dark matter particles at and after thermal freeze-out, close-to-threshold processes need to be taken into account which have a large impact on the observed dark matter relic abundance.  Our aim is to study the recoil effect of kinetically equilibrated dark matter pairs in a thermal medium and compute the center-of-mass recoil corrections to the near-threshold observables in the laboratory frame within the framework of potential non-relativistic effective field theories at finite temperature.  For the considered hierarchy of energy scales, we highlight the relative corrections due the recoil on the present dark matter energy density.