Here, we report the first order martensite to austenite transition characterized through magnetic and calorimetric studies in (off-stoichiometric) shape memory Heusler alloy Ni45Mn44Sn11-XInX (X = 1; 3) in the proximity of room temperature. The structural properties of the alloys were checked with x-ray diffraction (XRD), x-ray photoemission spectroscopy (XPS) and energy dispersive x-ray analysis (EDXA). The dominance of a particular phase (martensite or austenite) at room temperature can be predicted from the structural study by XRD as two different phases (L21 and 10 M) were found at room temperature with different proportion for the two alloys. Martensite transition was observed near the room temperature for both samples which was monitored with differential calorimetry and magnetization study. A large magneto-caloric effect was found in the system near the room temperature observed from the magnetic measurements. The calculated entropy change (3.24 JKg−1K−1 and 11.2 JKg−1K−1 for X = 1 and 3 respectively) and the refrigerant capacity (27 JKg−1 and 40 JKg−1 for X = 1 and 3 respectively) for 3 T magnetic field were found to be significant for practical applications near room temperature. A small amount of In substitutions in Sn sites have influenced the martensite transition as a significant increase in the martensite transition temperature has been observed. The magnetocaloric effect in these materials has been understood in the realm of sharp magnetization change arising in the vicinity of metamagnetic transition from the martensite phase (weakly magnetic) to the austenite phase (ferromagnetic). The In substitution is thought to influence the hybridization between Ni-Mn bonds which in turn influence the martensite transition and thereby enhancing the magnetocaloric property of the materials.