  The puzzling observation of room temperature ferromagnetism in double
perovskites (A$_2$BB$'$O$_6$), despite having the magnetic lattice of B-ions
diluted by non-magnetic B$'$-ions, have been examined for Sr$_2$FeReO$_6$. {\it
Ab-initio} spin spiral electronic structure calculations along various high
symmetry directions in reciprocal space are used to determine the exchange
interactions entering an extended Heisenberg model, which is then solved
classically using Monte Carlo simulations to determine the ferromagnetic
transition temperature T$_c$. We find that one must consider onsite Coulomb
interactions at the nonmagnetic Re sites ($U$) in order to obtain a T$_c$ close
to the experimental value. Analysis of the $ab$-$initio$ electronic structure
as well as an appropriate model Hamiltonian trace the origin of enhancement in
T$_c$ with $U$ to the enhanced exchange splitting that is introduced at these
sites. This in turn destabilizes the antiferromagnetic exchange channels,
thereby enhancing the T$_c$. The role of occupancy at the non-magnetic sites is
examined by contrasting with the case of Sr$_2$FeMoO$_6$.
