  We report on measurements of the adiabatic temperature change in the inverse
magnetocaloric Ni$_{50}$Mn$_{34}$In$_{16}$ alloy. It is shown that this alloy
heats up with the application of a magnetic field around the Curie point due to
the conventional magnetocaloric effect. In contrast, the inverse magnetocaloric
effect associated with the martensitic transition results in the unusual
decrease of temperature by adiabatic magnetization. We also provide
magnetization and specific heat data which enable to compare the measured
temperature changes to the values indirectly computed from thermodynamic
relationships. Good agreement is obtained for the conventional effect at the
second-order paramagnetic-ferromagnetic phase transition. However, at the first
order structural transition the measured values at high fields are lower than
the computed ones. Irreversible thermodynamics arguments are given to show that
such a discrepancy is due to the irreversibility of the first-order martensitic
transition.
