The unavoidable existence of thermal hysteresis in magnetocaloric materials with a first-order phase transition is one of the central problems limiting their implementation in cooling devices. Using minor loops, however, allows achieving significant cyclic effects even in materials with relatively large hysteresis. Here, we compare thermometric measurements of the adiabatic temperature change ΔTad and calorimetric measurements of the isothermal entropy change ΔST when moving in minor hysteresis loops driven by magnetic fields. Under cycling in 2 T, the Ni-Mn-In-Co Heusler material provides a reversible magnetocaloric effect of ΔSrevT = 10.5 J kg-1K-1 and ΔTrevad = 3.0 K. Even though the thermodynamic conditions and time scales are very different in adiabatic and isothermal minor loops, it turns out that after a suitable scaling, a self-consistent reversibility region in the entropy diagram is found. This region is larger than expected from basic thermodynamic considerations based on isofield measurements alone, which opens new opportunities in application. [ABSTRACT FROM AUTHOR]