  We present a comprehensive theory of the temperature- and disorder-dependence
of half-metallic ferrimagnetism in the double perovskite Sr$_2$FeMoO$_6$ (SFMO)
with $T_c$ above room temperature. We show that the magnetization $M(T)$ and
conduction electron polarization $P(T)$ are both proportional to the
magnetization $M_S(T)$ of localized Fe spins. We derive and validate an
effective spin Hamiltonian, amenable to large-scale three-dimensional
simulations. We show how $M(T)$ and $T_c$ are affected by disorder, ubiquitous
in these materials. We suggest a way to enhance $T_c$ in SFMO without
sacrificing polarization.
