We have studied the magnetocaloric effect (MCE) in the shape-memory Heusler alloy Ni₅₀Mn₃₅In₁₅ by direct measurements in pulsed magnetic fields up to 6 and 20 T. The results in 6 T are compared with data obtained from heat-capacity experiments. We find a saturation of the inverse MCE, related to the first-order martensitic transition, with a maximum adiabatic temperature change of ΔT_ad = -7 K at 250 K and a conventional field-dependent MCE near the second-order ferromagnetic transition in the austenitic phase. The pulsed magnetic field data allow for an analysis of the temperature response of the sample to the magnetic field on a time scale of ∼10 to 100 ms, which is on the order of typical operation frequencies (10-100 Hz) of magnetocaloric cooling devices. Our results disclose that in shape-memory alloys, the different contributions to the MCE and hysteresis effects around the martensitic transition have to be carefully considered for future cooling applications.