The non-stoichiometric Heusler alloy Ni$_{50}$Mn$_{36}$In$_{14}$ undergoes a martensitic phase transformation in the vicinity of 345 K, with the high temperature austenite phase exhibiting paramagnetic rather than ferromagnetic behavior, as shown in similar alloys with lower-temperature transformations. Suitably prepared samples are shown to exhibit a sharp transformation, a relatively small thermal hysteresis, and a large field-induced entropy change. We analyzed the magnetocaloric behavior both through magnetization and direct field-dependent calorimetry measurements. For measurements passing through the first-order transformation, an improved method for heat-pulse relaxation calorimetry was designed. The results provide a firm basis for the analytic evaluation of field-induced entropy changes in related materials. An analysis of the relative cooling power (RCP), based on the integrated field-induced entropy change and magnetizing behavior of the Mn spin system with ferromagnetic correlations, shows that a significant RCP may be obtained in these materials by tuning the magnetic and structural transformation temperatures through minor compositional changes or local order changes.