Positron cooling via inelastic collisions in CF$_4$ and N$_2$ gases is simulated, including positron-positron interactions. Owing to the molecular symmetries, cooling is assumed to be chiefly due to energy loss via vibrational (rotational) excitations for CF$_4$ (N$_2$). For CF$_4$, it is found that the inclusion of the dipole-inactive $ u_1$ mode, in addition to the dipole-active modes $ u_3$ and $ u_4$, can provide room-temperature thermalization and an accurate cooling timescale. Combination cooling enabled by the $ u_1$ mode, and positron-positron interactions both contribute to the Maxwellianization of the positron momentum distribution. For both gases the evolution of the positron temperature is found to be in excellent agreement with experiment.
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