  We observe a crossover from electron-phonon (ep) coupling limited energy
relaxation to that governed by thermal boundary resistance (pp) in copper films
at sub-kelvin temperatures. Our measurement yields a quantitative picture of
heat currents, in terms of temperature dependences and magnitudes, in both ep
and pp limited regimes, respectively. We show that by adding a third layer in
between the copper film and the substrate, the thermal boundary resistance is
increased fourfold, consistent with an assumed series connection of thermal
resistances.
