  We discuss a sympathetic cooling strategy that can successfully mitigate
fermion-hole heating in a dilute atomic Fermi-Bose mixture and access the
temperature regime in which the fermions behave as a Fermi liquid. We introduce
an energy-based formalism to describe the temperature dynamics with which we
study a specific and promising mixture composed of 6Li and 87Rb. Analyzing the
harmonically trapped mixture, we find that the favourable features of this
mixture are further enhanced by using different trapping frequencies for the
two species.
