Hot electrons in metals at helium temperatures under steady conditions can be produced by passing an electric current of moderate density (≲ 106 A/cm2) through thin, narrow (~1 Μm wide) metallic films in good thermal contact with bulk single-crystal dielectric substrates. This paper is concerned with the theory of hot electrons in normal metals at low temperatures (when θ ≪ θD, where θ is the average electron energy and θD is the Debye temperature). The theory is formulated in terms of realistic electron and phonon dispersion laws, taking into account the experimental possibility of heat removal from the sample. In the case in which the temperature approximation of Kagnov, Lifshitz, and Tanatarov is not satisfied when elastic scattering of electrons is dominant in a steady state electric field, the kinetic equation is derived for the energy-dependent, hot electron distribution function, which determines the associated nonlinear responses. The solution of this equation is discussed for a simple model. It is shown that the experimental information on the electron-phonon interaction in a metal can be obtained in terms of the well-known spectral functions S(Ω) ≡ α2F(Ω) and g(Ω) ≡ αtr2F(Ω). This is illustrated by experiments determining the nonlinear field dependence of the resistance, by tunnel experiments, and by critical current hysteresis measurements (for superconducting metals). Theoretical estimates which support the observability of the effects under discussion are presented.