Here we report on compressive stress-strain behavior, ordinary and burst-like shape memory (SM) strain recovery, and associated caloric effects in Cu – 14.02% wt. Al – 4.0% wt. Ni single crystals which have multiphase martensitic structure at room temperature. The effect of repetitive thermo-mechanical cycling on the recovery of the shape memory deformation is investigated. The stress-strain curves of the specimens are smooth in all tests. Immediately after quenching, crystals exhibited burst-like strain recovery accompanied by the jumping of the whole specimen in each deformation-recovery. After several days from quenching, crystals showed weaker jumping which was also reducing with each thermo-mechanical cycle. The average values of the integral thermal effect remained the same from cycle to cycle. Although the starting temperature of burst-like reverse martensitic transformation stochastically varied from cycle to cycle, it showed a general tendency to decrease with an increasing number of cycles until the burst-like effect disappears completely. The heating rate does not significantly affect the position of the DSC peak. Low temperature aging of the specimens resulted in the gradual weakening and disappearance of the burst-like strain recovery. Thus, thermal treatment and loading regimes should be optimized for high-cycle applications of Cu-Al-Ni alloys.