[en] Earlier work on electron thermalization in rare gases by the author [J. Chem. Phys. 72, 1657 (1980); 72, 6289 (1980)] has been extended to include electron scavenging by an attaching compound present as a minor component. While the cooling rate for the surviving fraction proceeds as in the pure gas, the scavenging rate is calculated using a time-dependent velocity distribution function and a velocity-dependent attachment cross section. For the last mentioned item, functions decreasing with a certain power of velocity specific to a given scavenger have been experimentally found by Christophorou and co-workers; the same are used with analytical extension. In general, epithermal scavenging has been found to be ubiquitous and time dependent. It depends mainly on the thermalization time, relative scavenger concentration, temperature, and thermal attachment cross section. Relative scavenger effectiveness has been found to be temperature dependent. In a simple case autodetachment has been included in the calculation using SF₆ as an example. Both attachment and detachment compete with thermalization, the equilibrium being established only in the postthermal regime. To ensure purely thermal reactions in a rare gas such as Ar, which has the longest thermalization time of all the rare gases, purification from reactive scavengers must be carried to the level of 1 ppb (part per billion) or better. For other rare gases the requirement may be less stringent