  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 $T_c$.
