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Among NiMnGa-based quaternary systems, NiMnGaCu exhibits an interesting giant magnetocaloric effect thanks to the temperature overlapping of magnetic transition and thermoelastic martensitic transformation (TMT), in particular for compositions with ≈6 at% Cu content. In the present work polycrystalline alloy samples with Ni50Mn18.5Cu6.5Ga25 chemical composition were prepared. We present an extensive calorimetric and structural characterization to explore the correlation between microstructural properties and magnetocaloric response induced by means of selected thermal treatments, likely driven by the contribution of TMT to the magnetocaloric effect. Our results give important hints on how the efficiency of the martensitic transition and its modulation in temperature has a final effect on the total ΔS change. Keywords: Magnetic Shape Memory Alloys, Calorimetric investigation, Thermoelastic martensitic transition, Magnetocaloric effect, Thermal treatment, NiMnGaCu