Heusler Ni-Mn-Sn-based alloys are good candidates for magnetic refrigeration. This application is based on cycling processes. In this work, thermal cycles (100) have been performed in three ribbons produced by melt-spinning to check the thermal stability and the magnetic response. After cycling, the temperatures were slowly shifted and the thermodynamic properties were reduced, the entropy changed at about 3–5%. Likewise, the thermomagnetic response remains similar. Thus, these candidates maintain enough thermal stability and magnetic response after cycling. Likewise, Cu addition shifts the structural transformation to higher temperatures, whereas the Curie temperature is always near 310 K. Regarding magnetic shape memory applications, the best candidate is the Ni49Mn36 Sn14Cu1 alloy.