A new experimental study of A(s) and M(s) in the Fe-Mn system has been performed by using two complementary experimental techniques, viz., dilatometry and electrical resistivity measurements, which are applied to the whole composition range where the transformation can be detected, i.e., between 10 and 30 pet Mn. We used the A(s) and M(s) temperatures as input information in an analysis based on thermodynamic models for the Gibbs energy of the face-centered cubic (fcc) and hexagonal close-packed (hcp) phases. In these models, the magnetic contribution to Gibbs energy is accounted for, which allows us to study, by calculation, the influence of the entropy of magnetic ordering upon the relative stability of the phases. The picture of magnetic effects upon the fcc/hcp transformation that emerges from our work is as follows. At low Mn contents, the martensitic transformation temperatures are larger than the Neel temperature of the fcc phase, and both A(s) and M(s) decrease linearly with increasing Mn. This encourages an extrapolation to zero Mn content, and we use that to critically discuss the available information on the fcc/hcp equilibrium temperature for Fe at atmospheric pressure. At sufficiently large Mn contents, we have M(s) < T-N(gamma) which implies that the fcc phase orders antiferromagnetically before transforming to the hcp phase. Since hcp remains paramagnetic down to lower temperatures, the ordering reaction in fee leads to a relative stabilization of this phase, which is reflected in a drastic, nonlinear decrease of M(s).