TiNiCu-based superelastic alloys are promising for use as elastocaloric materials. In this study, we aim to produce a TiNiCuNb alloy with a refined microstructure, adequate Af, and latent heat for room-temperature application. For that, a Ti48Ni38Cu10Nb4 alloy was produced via arc melting followed by fast-cooling vacuum-suction casting (SC). Compared to the material that was only arc-melted, a refined and more uniform microstructure was obtained. This microstructure exhibited high stability during superelastic cycling and an Af much lower than room temperature. Further thermomechanical processing and heat-treatment (HT) were used to adjust the martensitic transformation (MT) critical temperatures and enthalpy. Increasing Af and enthalpy were observed with increasing HT temperatures. It was discussed that, besides the effect of the development of recovery/recrystallization mechanisms, the Nb content in the TiNi matrix could impact these properties. An Af close to, but smaller than room temperature, was obtained for the alloy heat-treated at 450 °C, with a MT enthalpy of 9.9 J/g.