Micro-electromechanical systems (MEMS) are often subject to mechanical vibration or temperature, the fatigue reliability of small metal parts is a potential problem for long-term operational stability. Since the MEMS packaging is performed at a high temperature of about 600 K. Therefore, in this paper, the deformation mechanisms of copper nano-single crystals with different surface morphologies under cyclic loading were investigated by molecular dynamics calculations at room temperature (300 K) and high temperature (600 K) to provide a theoretical basis for the design of copper nanomaterials. The results show that the plastic deformation modes of the models with different surface morphologies during cyclic loading are mainly Shockley partial dislocations slipping along {111}. In contrast, the fatigue damage modes are extrusion intrusion induced by high shear strain. Compared with the surface containing a pore, the damage caused by the circular and sharp recesses through the surface is more serious. The causes of stress concentration during deformation are mainly the entanglement of Shockley partial dislocations and the generation of Lomer-Corell lock fixed dislocations. The locations of these stress concentrations will produce pores in the subsequent deformation. In addition, since periodic interfaces do not cause particularly pronounced stress concentrations and shear strain concentrations on the surface compared to other models with defects, and the resulting shear strain concentration bands are split by shear strain bands in the other direction, extrusion intrusion is prevented. Therefore, at room temperature, the model with a one-dimensional sinusoidal surface has the strongest resistance to fatigue damage, while at high temperatures, the model with a two-dimensional sinusoidal surface has the optimal resistance to fatigue damage. This provides a basis for the design of NEMS/MEMS working at high temperatures.