  We have used symmetric normal metal-insulator-superconductor (NIS) tunnel
junction pairs, known as SINIS structures, for ultrasensitive thermometry in
the temperature range 50 - 700 mK. By Joule heating the electron gas and
measuring the electron temperature, we show that the electron-phonon (e-p)
scattering rate in the simplest noble metal disordered thin films (Cu,Au)
follows a $T^4$ temperature dependence, leading to a stronger decoupling of the
electron gas from the lattice at the lowest temperatures. This power law is
indicative e-p coupling mediated by vibrating disorder, in contrast to the
previously observed $T^3$ and $T^2$ laws.
