  Multi-temperature models are nowadays often used to quantify the ultrafast
electron-phonon (boson) relaxations and coupling strengths in advanced quantum
solids. To test their applicability we study the time evolution of the electron
distribution function, f(E), in Cu over large range of excitation densities
using broadband time-resolved optical spectroscopy. Following intraband optical
excitation, f(E) is found to be athermal over several 100 fs, while substantial
part of the absorbed energy already being transferred to the lattice. We show,
however, that the electron-phonon coupling constant can still be obtained using
the two-temperature model analysis, provided that the data are analyzed over
the time-window, when the electrons are already quasi thermal, and the
electronic temperature is determined experimentally.
