  We investigate the temporal and spatial scales of resistance fluctuations
(R-fluctuations) at the superconducting resistive transition accessed through
voltage fluctuations measurements in thin epitaxial TiN films. This material is
characterized by a record slow electron-phonon relaxation, which puts it far
beyond the applicability range of the textbook scenario of superconducting
fluctuations. The measured Lorentzian spectrum of the R-fluctuations identifies
their correlation time, which is nearly constant across the transition region
and has no relation to the conventional Ginzburg-Landau time scale. Instead,
the correlation time coincides with the energy relaxation time determined by a
combination of the electron-phonon relaxation and the diffusion in reservoirs.
Our data is quantitatively consistent with the model of spontaneous temperature
fluctuations and highlight important caveats in the accepted physical picture
of the resistive transition in materials with slow electron-phonon relaxation.
