  The two-temperature model (2TM) introduced by Kaganov, Lifshitz, and
Tanatarov is widely used to describe the energy relaxation in the
electron-phonon system of a metallic film. At the same time, the accuracy of
the description of the electron-phonon system in terms of 2TM, i.e. on the
basis of the electron and phonon temperatures, has not been considered in
detail until now. In this paper we present a microscopic theory of cooling of
instantly heated electrons in metallic films. In framework of this theory the
main features of electron cooling in thick and thin films were found, and an
analysis of the accuracy of the 2TM in the low-temperature region was carried
out. We consider a more accurate three-temperature model, which (in contrast to
2TM) explicitly takes into account phonons with angles of incidence exceeding
the angle of total internal reflection. The contribution of these phonons to
the kinetics of electron relaxation can be significant if the sound velocities
in the film and the substrate are quite different.
