Magnetic Cluster Expansion model is developed for bcc Fe-Cr alloys, and applied to the investigation of magnetic properties of these alloys for a broad interval of concentrations ranging from pure Fe to pure Cr, and for a broad interval of temperatures extending well over 1000 K. Finite-temperature configurations simulated using the Magnetic Cluster Expansion Hamiltonian describe various magnetically ordered ferromagnetic and antiferromagnetic phases, partially magnetically ordered phases, and transitions between them and paramagnetic phases. We investigate the dependence of the Curie and Néel transition temperatures on the composition of the alloy. Analysis of the magnetic specific heat treated as a function of Cr concentration shows that in the low Cr concentration limit the Curie temperature increases as a function of Cr content. We find that for alloys containing high level of Cr the Curie temperature depends sensitively on the degree of Cr precipitation, varying by as much as 150K between random alloy configurations and configurations containing Cr precipitates.