We report the effect of Ni substitution on the magnetic properties of polycrystalline Ni2+xMn1−xSn (x = 0, 0.05, and 0.1) Heusler alloys using the magnetization and neutron diffraction measurement techniques. The paramagnetic to ferromagnetic transition temperature (Curie temperature, TC) has been tuned with the substitution of Ni at the Mn sites (TC≈ 349, 337, and 317 K for x = 0, 0.05, and 0.1 samples, respectively) without a significant reduction in the magnetic entropy change −ΔSM. For a magnetic field change from 0 to 5 T, −ΔSM of 2.9, 2.5, and 2.2 J kg−1 K−1 have been observed for x = 0, 0.05, and 0.1 samples, respectively. From the neutron diffraction study, it has been found that with increasing x, the Mn site ordered moment decreases. −ΔSM as a function of changing magnetic field and Curie temperature follows the molecular mean field model. The studied Ni2+xMn1−xSn alloys, with their nontoxic constituent elements and low-cost, can be used for magnetic cooling over a wide temperature range of 278–379 K covering room temperature.