The influence of tensile stresses coupled with temperature cycling has been determined on a Cu-Zn-Al shape memory alloy that transforms above room temperature. It is shown that the application of increasing stresses during thermal cycles leads to an increasing martensite stabilization. The repeated thermal cycling with constant stress as well as slow temperature rates increase the stabilization. This phenomenon is attributed to a pinning of austenite-martensite interfaces by vacancies. This hypothesis is confirmed by the comparison of experiments with continuous and with stepwise temperature variations.