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The puzzling observation of room temperature ferromagnetism in doubleperovskites (A$_2$BB$'$O$_6$), despite having the magnetic lattice of B-ionsdiluted by non-magnetic B$'$-ions, have been examined for Sr$_2$FeReO$_6$. {\itAb-initio} spin spiral electronic structure calculations along various highsymmetry directions in reciprocal space are used to determine the exchangeinteractions entering an extended Heisenberg model, which is then solvedclassically using Monte Carlo simulations to determine the ferromagnetictransition temperature T$_c$. We find that one must consider onsite Coulombinteractions at the nonmagnetic Re sites ($U$) in order to obtain a T$_c$ closeto the experimental value. Analysis of the $ab$-$initio$ electronic structureas well as an appropriate model Hamiltonian trace the origin of enhancement inT$_c$ with $U$ to the enhanced exchange splitting that is introduced at thesesites. This in turn destabilizes the antiferromagnetic exchange channels,thereby enhancing the T$_c$. The role of occupancy at the non-magnetic sites isexamined by contrasting with the case of Sr$_2$FeMoO$_6$.

Microscopic Origin Of Room Temperature Ferromagnetism in a Double Perovskite Sr$_2$FeReO$_6$: a first principle and model Hamiltonian study