  We report on the inelastic-scattering rate of electrons on phonons and
relaxation of electron energy studied by means of magnetoconductance, and
photoresponse, respectively, in a series of strongly disordered superconducting
NbN films. The studied films with thicknesses in the range from 3 to 33 nm are
characterized by different Ioffe-Regel parameters but an almost constant
product q_Tl(q_T is the wave vector of thermal phonons and l is the elastic
mean free path of electrons). In the temperature range 14-30 K, the
electron-phonon scattering rates obey temperature dependencies close to the
power law 1/\tau_{e-ph} \sim T^n with the exponents n = 3.2-3.8. We found that
in this temperature range \tau_{e-ph} and n of studied films vary weakly with
the thickness and square resistance. At 10 K electron-phonon scattering times
are in the range 11.9-17.5 ps. The data extracted from magnetoconductance
measurements were used to describe the experimental photoresponse with the
two-temperature model. For thick films, the photoresponse is reasonably well
described without fitting parameters, however, for thinner films, the fit
requires a smaller heat capacity of phonons. We attribute this finding to the
reduced density of phonon states in thin films at low temperatures. We also
show that the estimated Debye temperature in the studied NbN films is
noticeably smaller than in bulk material.

Superconductivity