  We consider a gas of cold fermionic atoms having two spin components with
interactions characterized by their s-wave scattering length $a$. At positive
scattering length the atoms form weakly bound bosonic molecules which can be
evaporatively cooled to undergo Bose-Einstein condensation, whereas at negative
scattering length BCS pairing can take place. It is shown that, by
adiabatically tuning the scattering length $a$ from positive to negative
values, one may transform the molecular Bose-Einstein condensate into a highly
degenerate atomic Fermi gas, with the ratio of temperature to Fermi temperature
$T/T_F \sim 10^{-2}$. The corresponding critical final value of $k_{F}|a|$
which leads to the BCS transition is found to be about one half, where $k_F$ is
the Fermi momentum.
