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Ni-Mn-based Heusler alloys, in particular all-d-metal Ni(-Co)-Mn-Ti, are highly promising materials for energy-efficient solid-state refrigeration as large multicaloric effects can be achieved across their magnetostructural martensitic transformation. However, no comprehensive study on the crucially important transition entropy change Δs exists so far for Ni(-Co)-Mn-Ti. Here, we present a systematic study analyzing the composition and temperature dependence of Δst. Our results reveal a substantial structural entropy change contribution of approximately 65 J(kgK)-1, which is compensated at lower temperatures by an increasingly negative entropy change associated with the magnetic subsystem. This leads to compensation temperatures Tcomp of 75 K and 300 K in Ni35Co15Mn50-yTiy and Ni33Co17Mn50-yTiy, respectively, below which the martensitic transformations are arrested. In addition, we simultaneously measured the responses of the magnetic, structural and electronic subsystems to the temperature- and field-induced martensitic transformation near Tcomp, showing an abnormal increase of hysteresis and consequently dissipation energy at cryogenic temperatures. Simultaneous measurements of magnetization and adiabatic temperature change ΔTad in pulsed magnetic fields reveal a change in sign of ΔTad and a substantial positive and irreversible ΔTad up to 15 K at 15 K as a consequence of increased dissipation losses and decreased heat capacity. Most importantly, this phenomenon is universal, it applies to any first-order material with non-negligible hysteresis and any stimulus, effectively limiting the utilization of their caloric effects for gas liquefaction at cryogenic temperatures.