Shape memory alloys (SMAs) and ferromagnetic shape memory alloys (FeSMAs) have recently attracted interest for solid state refrigeration applications. Among NiMnGa-based quaternary systems, NiMnGaCu exhibits an interesting giant magnetocaloric effect thanks to the overlapping of the temperatures related to the magnetic transition and the thermoelastic martensitic transformation (TMT); in particular, for compositions with Cu content of approximately 6 at%. In the present work, we investigated the improvement effect of TMT on the total entropy change (ΔS) in the elastocaloric performances of polycrystalline Ni50Mn18.5Cu6.5Ga25 at% alloy samples, just above room temperature. We report an extensive calorimetric and thermomechanical characterization to explore correlations between microstructural properties induced by the selected thermal treatment and elastocaloric response, aiming at providing the basis to develop more efficient materials based on this quaternary system. Both ΔT and ΔS values obtained from mechanical curves at different temperatures and strain recovery tests under fixed load vs. T were considered. Maximum values of ΔS = 55.9 J/KgK and ΔT = 4.5 K were attained with, respectively, a stress of 65 MPa and strain of 4%. The evaluation of the coefficient of performance (COP) was carried out from a cyclic test.