This article reports positron annihilation spectroscopy and calorimetric measurements of the aging behavior in a Cu¿Al¿Be shape memory alloy. An excess of single vacancies is retained in the alloy as a result of a quench. All vacancies in excess disappear after long aging time, and a migration energy EM = 1.0±0.1 eV for this process has been found to be larger than in other Cu-based shape memory alloys. The good correlation found for the concentration of vacancies and the shift in the martensitic transition temperature demonstrates that, in Cu¿Al¿Be, changes in the transition after a quench are deeply related to the excess of vacancies.