  Color superconductivity is a possible phase of high density QCD. We present a
systematic derivation of the transition temperature, T_C, from the QCD
Lagrangian through study of the di-quark proper vertex. With this approach, we
confirm the dependence of T_C on the coupling g, namely $T_C \sim \mu g^{-5}
e^{-\kappa/g}$, previously obtained from the one-gluon exchange approximation
in the superconducting phase. The diagrammatic approach we employ allows us to
examine the perturbative expansion of the vertex and the propagators. We find
an additional O(1) contribution to the prefactor of the exponential from the
one-loop quark self energy and that the other one-loop radiative contributions
and the two gluon exchange vertex contribution are subleading.
