Fe-Mn-Si based alloys exhibit the shape memory effect depending on their composition. Upon cooling, these alloys undergo a martensitic transformation gamma (fcc) --> epsilon (hcp), and a magnetic transition, at the Neel temperature, from paramagnetic to antiferromagnetic ordering in the gamma-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 gamma-phase. Consequently, the amount of thermally induced E-martensite was very small. Mossbauer spectroscopy and X-ray diffraction measurements showed that only 10% of epsilon-martensite was formed upon cooling to quite low temperatures.