The time evolution and temperature dependence of electron energy distribution functions (EDFs) are studied in pure rare gases (He, Ne, Ar, Kr, Xe) as well as in their mixtures by using solutions of the Boltzmann equation. A clear difference between the gases having the Ramsauer-Townsend (RT) minimum in the momentum-transfer cross section, (RT gases : Ar, Kr, and Xe), and those without the RT minimum (non-RT gases : He and Ne) is pointed out. The influence of the position and the depth of the RT minimum on the EDF and time evolution is studied for three different initial electron energies. A formula proposed for describing thermalization time in a mixture is tested on (i) a non-RT-non-RT gas mixture, (ii) a RT-non-RT mixture and (iii) a RT-RT gas mixture. The linear combination of the reciprocal thermalization times in gas mixture with the component concentrations as weighting factors is found to be valid for gases with a similar energy dependence of the momentum-transfer cross section, a,, and also for all rare-gas binary mixtures if the initial electron energy is sufficiently below the RT minimum. Conspicuous deviations from the linear relationship are observed in mixtures of gases whose energy dependence of a, (or the stopping cross section) are different, and theoretical rationales for these findings are provided.