The rate of hot-electron energy loss to the lattice in polar semiconductors is studied within a two-temperature model. We call attention to the role of the internal thermalization of the LO-phonon system in implementing this model and in establishing the concept of electron energy loss to phonons. With the help of the Feynman diagrammatic technique for the Keldysh closed-time-path Green's function, we have derived a formula for the electron-energy-loss rate, taking account of contributions from all orders of the electron-phonon interaction and including the hot-phonon effect. This formula, which carries the internal thermalization time of the LO-phonon system and the relaxation time of the whole lattice as parameters, reduces exactly to the conventional Kogan formula in the limit of weak electron-phonon coupling. In the zero-hot-phonon-effect Iimit (if it is allowed) this formula is shown to be equivalent to that given by Dharma-wardana [Phys. Rev. Lett. 66, 197(1991)]. Comparison beween our formula and that of Das Sarma and Korenman [Phys. Rev. Lett. 67, 2916(1991)] is also given. An interesting prediction of the present formula is the low-temperature enhancement of the electron-energy-loss rate over the conventional Kogan result. A numerical calculation for a two-dimensional GaAs system shows agreement between this theory and the experimental trend.