Thermalization of hot electrons in molecular gases is described by a Boltzmann equation, with the Boltzmann operator consisting of a Fokker‐Plank operator for elastic processes and a difference operator for inelastic ones. The eigenvalue approach of Shizgal and co‐workers for a Fokker‐Plank equation is extended to solve this Boltzmann equation. The inelastic interaction is much stronger than the elastic one, and two well‐separated time scales are involved in the relaxation processes. This makes the analysis difficult, and the convergence of the eigenmode expansion is very slow. It is shown, however, that a high precision calculation involving a few hundred eigenmodes shows convergence.