  We present a semi-analytic theory for the Curie temperature in diluted
magnetic semi-conductors that treats disorder effects exactly in the effective
Heisenberg Hamiltonian, and spin fluctuations within a local RPA. The exchange
couplings are taken from concentration dependent {\it ab initio} estimates. The
theory gives very good agreement with published data for well-annealed samples
of Mn$_x$Ga$_{1-x}$As. We predict the critical temperatures for
Mn$_x$Ga$_{1-x}$N lower than in doped GaAs, despite the stronger
nearest-neighbour ferromagnetic coupling. We also predict the dependence on the
hole concentration.
