  We investigate the effects of topological order on the transition
temperature, $T_c$, and response functions in fermionic superfluids with Rashba
spin-orbit coupling and a transverse Zeeman field in three dimensions. Our
calculations, relevant to the ultracold atomic Fermi gases, include
fluctuations beyond mean-field theory and are compatible with $f$-sum rules.
Reminiscent of the $p_x + i p_y$ superfluid, the topological phase is
stabilized when driven away from the Bose-Einstein condensation and towards the
BCS limit. Accordingly, while experimentally accessible, $T_c$ is significantly
suppressed in a topological superfluid. Above $T_c$, the spin and density
response functions provide signatures of topological phases via the
recombination or amplification of frequency dependent peaks.
