Equations for the coefficient of attenuation of radiation due to Compton scattering by a thermal electron gas with an arbitrary temperature are summarized. A new representation is also obtained for the integral through which the attenuation coefficient, averaged over a relativistic, Maxwellian energy distribution of electrons, is expressed. This representation enables one to efficiently calculate the coefficient for a high-temperature electron gas. The accuracy of an approximate expression for the attenuation coefficient, corresponding to the assumption that scattering is isotropic in the rest frame of an electron, is also estimated. ©2000 Kluwer Academic/Plenum Publishers.