We study both the time dependence and steady state of the coupled electron-phonon system in a thin metallic film, which provides a source of high energy phonons generated by Joule heating. The interface problem is included through a phenomenological relaxation time involving an acoustic mismatch parameter η. The detailed form of the phonon distribution is shown to be a non Bose like distribution. A phonon temperature Tp(q) defined in each mode is seen to deviate significantly from the electron temperature Te characterizing the Fermi-Dirac distribution. We show that the electrons see an essentially equilibrium phonon distribution at the ambient temperature (4.2 °K). We compare our model with the « one temperature model » in the black body limit