This study presents the heat treatment effect on a quaternary Cu79Al13Ni4Ta4 (wt%) shape memory alloy. The induction technique was used for melting the alloy and then four pieces of the alloy were heat-treated at (673 K, 873 K, 1073 K, and 1273 K) for one hour. Some physical parameters were characterized using DSC, XRD, and SEM-EDX. The as-cast and heat-treated samples were studied in terms of phase transformation temperatures, enthalpy change, entropy change, Gibbs free energy, and elastic energy. The transformation temperature was increased by applying heat treatment. Martensitic phase transformation at heat treatment temperature of 1273 K was not observed. Besides, after rising heat treatment temperature, some new phases such as Upsilon(1)' and beta(1)' were specified in XRD patterns and SEM images. Generally, for heat-treated samples, the transformation temperature remains almost constant after the 3rd cycle. However, the thermal stability of the as-cast alloy was not affected through thermal cycling.