We consider the superfluid phase transition that arises when a Feshbach res
onance pairing occurs in a dilute Fermi gas. We apply our theory to conside
r a specific resonance in potassium (K-40), and find that for achievable ex
perimental conditions, the transition to a superfluid phase is possible at
the high critical temperature of about 0.5T(F). Observation of superfluidit
y in this regime would provide the opportunity to experimentally study the
crossover from the superfluid phase of weakly coupled fermions to the Bose-
Einstein condensation of strongly bound composite bosons.