We formulate a theory of double perovskite coumpounds such as Sr$_2$FeReO$_6$ and Sr$_2$FeMoO$_6$ which have attracted recent attention for their possible uses as spin valves and sources of spin polarized electrons. We solve the theory in the dynamical mean field approximation to find the magnetic transition temperature $T_c$. We find that $T_c$ is determined by a subtle interplay between carrier density and the Fe-Mo/Re site energy difference, and that the non-Fe same-sublattice hopping acts to reduce $T_c$. Our results suggest that presently existing materials do not optimize $T_c$.