  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 $\nu_1$ mode, in addition to the dipole-active
modes $\nu_3$ and $\nu_4$, can provide room-temperature thermalization and an
accurate cooling timescale. Combination cooling enabled by the $\nu_1$ 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.
