Fe-Mn-Si based alloys exhibit the shape memory effect depending on their composition. Upon cooling, these alloys undergo a martensitic transformation γ (fcc) → ε (hcp), and a magnetic transition, at the Néel temperature, from paramagnetic to antiferromagnetic ordering in the γ-phase. In this work, the structural and magnetic phase transition temperatures were determined in an Fe-27Mn-2.5Si (in weight %) shape-memory alloy, using differential scanning calorimetry, dilatometry, electrical resistivity, Mossbauer spectroscopy, and X-ray diffraction. The transition temperatures measured by the different techniques were almost the same. It was observed, by calorimetry and electrical resistivity measurements, that the magnetic transition temperature upon cooling was very close and slightly higher than that of the start of the martensitic transformation, thus promoting the stabilization of the γ-phase. Consequently, the amount of thermally induced ε-martensite was very small. Mössbauer spectroscopy and X-ray diffraction measurements showed that only 10% of ε-martensite was formed upon cooling to quite low temperatures.