  We present the derivation of kinetic formulas modeling the microscopic
interaction of a charged particle withing a molecular gas under effect of
thermal motion. Both elastic and inelastic processes are taken in account. The
results were verified to reproduce the non-thermal formulas when the target
molecule velocity is set to zero. A set of simulation is provided to highlight
the effects in Argon and Carbon tetrafluoride. Our results can applied in
Monte-Carlo simulation of particle drift at energies of the same order of the
thermal kinetic energy of the buffer gas.
