  We consider the BCS-BEC crossover for a system of trapped Fermi atoms at
finite temperature, both below and above the superfluid critical temperature,
by including fluctuations beyond mean field. We determine the superfluid
critical temperature and the pair-breaking temperature as functions of the
attractive interaction between Fermi atoms, from the weak- to the
strong-coupling limit (where bosonic molecules form as bound-fermion pairs).
Density profiles in the trap are also obtained for all temperatures and
couplings.
