The influence of thermal cycling between - 196 °C and 200 °C and equivalent heat treatment at 200 °C on the amplitude dependence of internal friction at room temperature has been studied in as cast Cu – Al - Mn shape memory alloys with different chemical compositions. Using X-ray diffraction one composition was found to be austenitic and two others martensitic with two martensite types (2H and 18R) at room temperature. All specimens were thermally cycled for 100 times. During one thermal cycle the specimen underwent altogether two phase transformations one in each direction. Thermal cycling causes microstructural changes in the specimens due to atomic reordering, thermal stresses, which are generated in the martensitic state due to the anisotropy of thermal expansion, or due to the nucleation and propagation of interphase cracks in parent phase. During repeated thermal cycling the transition peaks obtained in mechanical spectroscopy became narrower due to an enduring change of the microstructure and annealing effect at 200 °C. To compare between the effects of thermal cycling and heat treatment one martensitic specimen was annealed at 200 °C. For selected cycle numbers and heat treatment times the amplitude dependence of damping was measured at room temperature. The influence of thermal cycling of martensitic specimens on the damping level was found to be similar to the influence of heat treatment at 200 °C. It is most likely that the highest heat treatment temperature is more important for the amplitude dependence of damping than the temperature change during thermal cycling. Cracks due to thermal cycling were found in all cycled specimens. They have no significant effect on the amplitude dependence of damping of the martensitic samples, whereas some small influence could be observed in austenitic samples at room temperature.