  We determine the size of the critical region of the superfluid transition in
the BCS-BEC crossover of a three-dimensional fermion gas, using a
renormalization-group approach to a bosonic theory of pairing fluctuations. For
the unitary Fermi gas, we find a sizable critical region $[T_G^-,T_G^+]$, of
order $T_c$, around the transition temperature $T_c$ with a pronounced
asymmetry: $|T_G^+-T_c|/|T_G^--T_c|\sim8$. The critical region is strongly
suppressed on the BCS side of the crossover but remains important on the BEC
side.
