  We investigate the superfluid transition of the Unitary Fermi Gas by means of
the Functional Renormalization Group, aiming at quantitative precision. We
extract $T_{\rm c}/\mu=0.38(2)$ and $\Delta/\mu=1.04(15)$ for the critical
temperature and the superfluid gap at zero temperature, respectively, within a
systematic improvement of the truncation for the effective average action. The
key new ingredient in comparison to previous approaches consists in the use of
regulators which cut off both frequencies and momenta. We incorporate
renormalization effects on both the bosonic and the fermionic propagator,
include higher order bosonic scattering processes, and investigate the
regulator and specification parameter dependence for an error estimate. The
ratio $\Delta/T_{\rm c}=2.7(3)$ becomes less sensitive to the relative cutoff
scale of bosons and fermions when improving the truncation. The techniques
developed in this work are easily carried over to the cases of finite
scattering length, lower dimensionality, and spin-imbalance.
