This paper takes a deployable metamorphic robotic grasper as the studied object and its thermal-structural analysis with finite element method is carried out, by which the thermal deformation of the robotic grasper can be obtained and the optimization can be performed. As a result, the mechanical performance of the robotic grasper can be greatly enhanced, which is of great significance for the on-orbit operation of space spacecraft. Firstly, the robotic grasper is sample introduced and a theoretical model of the space temperature field is established, which offers a theoretical basis for finite element simulation. In addition, by finite element analysis software, an automatic mesh partition is applied and the finite element model of the robotic grasper is then established. By loading the temperature field, the thermal deformation can be shown, which provides a clear idea for structural optimization. Finally, through a large amount of simulation data, the most thermal deformation of the robotic grasper can be optimized, and then further simulation of the optimized model is carried out, the results show that the thermal deformation effectively decreases and the theoretical model is feasible.