Hot electrons and energy transport in metals at millikelvin temperatures

Using a new technique, we measure the energy-loss lifetime for electrons in a metal from 25 to 320 mK. Applying a small electric field, of order 1 \ensuremath{\mu}V/cm at 25 mK, causes carriers to heat above the temperature of the phonon bath. The temperature difference induced reflects the rate of energy transport between the electrons and lattice. The 1-ms energy-loss lifetime and 1-cm inelastic diffusion length we have measured at 25 mK are the largest ever obtained.