Large deployable cable net antennas have attracted extensive attention worldwide because of their simple structure and high storage ratio. The cable net structure is affected by long exposure in a harsh space environment during satellite operation, resulting in large thermal deformation and stress relaxation, which leads to a degradation of antenna performance. To address the thermal deformation of the cable net structure, a shape memory cable (SMC) net structure model was proposed with surface accuracy as the research objective. Specifically, we aimed to utilize its phase transition characteristics to adjust the thermal deformation of cable net structure and improve its surface accuracy. A shape memory cable net structure model with a diameter of 2.2 m was built, and a normal temperature experiment and high- and low-temperature experiments were carried out. High- and low-temperature test refers to environmental simulation testing of shape memory cable net structures under high- and low-temperature conditions. This was done to determine whether the adjustment method for surface accuracy meets the requirements. The results showed that the shape memory alloy wire has a relatively stable ability to adjust the surface accuracy of the cable net structure at room temperature. During temperature cycling, the thermal deformation of the shape memory cable net structure is slight, and the surface accuracy is good. Compared with ordinary cable net structures, the shape memory cable net structure has improved surface accuracy by 44.4% and 45.2% at high and low temperatures, respectively. This proved the effectiveness of the method for adjusting surface accuracy. These experimental results offer guiding significance for engineering applications.