  We study the sympathetic cooling of a trapped Fermi gas interacting with an
ideal Bose gas below the critical temperature of the Bose-Einstein
condensation. We derive the quantum master equation, which describes the
dynamics of the fermionic component, and postulating the thermal distribution
for both gases we calculate analytically the rate at which fermions are cooled
by the bosonic atoms. The particle losses constitute an important source of
heating of the degenerate Fermi gas. We evaluate the rate of loss-induced
heating and derive analytical results for the final temperature of fermions,
which is limited in the presence of particle losses.
