  We have studied the electron-phonon (e-p) interaction in thin Cu and Au films
at sub-Kelvin temperatures with the help of the hot electron effect, using
symmetric normal metal-insulator-superconductor tunnel junction pairs as
thermometers. By Joule heating the electron gas and measuring the electron and
the lattice temperatures simultaneously, we show that the electron-phonon
scattering rate follows a $T^{4}$ temperature dependence in both metals. The
result is in accordance with the theory of e-p scattering in disordered films
with vibrating boudaries and impurities, in contrast to the $T^{3}$-law
expected for pure samples, and $T^{2}$-law for static disorder.
