  In the framework of Keldysh-Usadel kinetic theory, we study the temperature
dependence of flux-flow conductivity (FFC) in diffusive superconductors. By
using self-consistent vortex solutions we find the exact values of
dimensionless parameters that determine the diffusion-controlled FFC both in
the limit of the low temperatures and close to the critical one. Taking into
account the electron-phonon scattering we study the transition between
flux-flow regimes controlled either by the diffusion or the inelastic
relaxation of non-equilibrium quasiparticles. We demonstrate that the inelastic
electron-phonon relaxation leads to the strong suppression of FFC as compared
to the previous estimates making it possible to obtain the numerical agreement
with experimental results.
