The efficiency of shape memory alloy (SMA) as damper and/or standard actuator is truly enhanced when the material can be cycled without any relevant accumulation of the permanent deformation (i.e. under 0.5% for several hundreds of cycles). The particular properties of the CuAlBe alloy permit relevant grain growth with reasonable reduction of mechanical properties (from 300–350 to 250–300 MPa at fracture). Samples prepared with an appropriate heat thermal treatment (HTT) and relevant mean diameter of grain avoids accumulative deformation for series of cycles (near 500) up to 3.5% of deformation. The analysis of different wires of CuAlBe alloy shows, in the first part of HTT, a proportionality between the grain surface and the time at 1123 K. In the last part of the HTT the grain growth shows an increased complexity related with interactions between the grain boundaries and the external surface of the samples.