Shape memory alloys are used in diverse fields. It is Ni–Ti alloys that are predominantly used for applications capitalizing on the functional properties of shape memory and superelastic effect. These properties are influenced by factors, such as alloy composition, alloying addition, thermal and mechanical treatment, etc. In any application, the transformation temperatures of the alloy/device are very critical. Moreover, the stability of transformation temperatures and a smaller hysteresis are preferred. Ni–Ti alloys have their own limitations, such as low transformation temperatures and lack of ductility. In order to overcome these limitations, researchers have used ternary additions, such as Zr, Hf, Cu, Pd and Au. The use of copper is practicable because of its lower cost as compared to Ti and Ni. Substitution of Cu for Ni up to 25% in an equiatomic NiTi alloy causes it to exhibit SME. The transformation temperatures of NiTiCu exhibit less sensitivity to composition and a smaller thermal hysteresis. In this work, therefore, the effect of methods of quenching on transformation temperatures and microstructure of an Ni–Ti–4Cu (at.%) alloy has been explored. The material was cast using vacuum induction melting. It was solutionized at 950 °C for 2 h and cooled using different methods/quenchants: liquid nitrogen, water at room temperature, air, annealing (furnace cooling). The samples quenched by different techniques were characterized by XRD, DSC, OM, SEM and hardness test. The results indicated that the martensite plate size varied in samples quenched using different quenchants even though the morphology was the same in all specimens. In addition, the transformation temperatures and hardness values of the alloy specimens varied as the intensity of quenching varied. The results are presented and discussed in detail in the paper. © 2020, The Indian Institute of Metals - IIM.