Among NiTi-based alloys, one of the most promising and exploited alloys is NiTiCu, since the addition of Cu in substitution of Ni in the binary equiatomic NiTi has a significant influence on the martensitic transformation and the thermomechanical properties of the system. A high content of Cu improves the damping properties at the expense of phase homogeneity and workability. The present study focuses on an alloy with a high copper content, i.e., 20 at.%. For this specific composition, the correlation between the thermal treatments, microstructure, formation of secondary phases, and damping properties are investigated by several analyses. The microscopic observation, together with the compositional analysis, allowed the determination of four different phases in the alloy. Both the calorimetry and dynamic thermo mechanical measurements, which confirmed the high damping ability of the alloy, provided a characterization of the martensitic transition. Finally, the electron backscatter diffraction (EBSD) analysis detected the different crystallographic structures (i.e., cubic austenite, orthorhombic martensite, and cubic (face-centered) NiTi2) and their orientation in the different phases. Therefore, the present work aims to improve the knowledge of the role of secondary phases in the optimization of the NiTiCu20 alloy as a valuable alternative to typical alloys used for damping purposes.