Little is known of the mechanism by which H and H2, the principal constituents of the post-re-combination early Universe, cooled sufficiently to permit cluster formation, nucleosynthesis, and, eventually, the formation of structured objects. Radiative decay primarily cools the internal modes of H2, as Δj = - 2 jumps accompany quadrupolar emission. This, however, would be a self-limiting mechanism. In this work, a translational energy cooling mechanism based on collision-induced, translation-to-internal mode conversion, is extended, following an earlier study [A. J. McCaffery and R. J. Marsh, J. Chem. Phys. 139, 234310 (2013)] of ensembles comprising H2 in a H atom bath gas. Here, the possible influence of minor species, such as HD, on this cooling mechanism is investigated. Results suggest that the influence of HD is small but not insignificant. Conversion is very rapid and an overall translation-to-internal energy conversion efficiency of some 5% could be expected. This finding may be of use in the further development of models of this complex phase of early Universe evolution. An unexpected finding in this study was that H2 + HD ensembles are capable of very rapid translation-to-internal conversion with efficiencies of >40% and relaxation rates that appear to be relatively slow. This may have potential as an energy storage mechanism.