A modular space deployable antenna has the advantages of extensibility, adaptability, and versatility, which is an ideal structure to meet the development trend of large aperture, high precision, and light weight for the deployable antenna in the future. To date, there are few reports on the temperature response of a modular deployable antenna in the thermal alternating environment in orbit. The aim of this study is at investigating the influence of a modular deployable antenna support structure on the surface accuracy and stability under the space thermal alternating environment. For this purpose, the thermal-structure analysis of the deployable antenna support structure was carried out by ANSYS APDL finite-element software. Using the transient temperature field obtained by thermal analysis as the boundary condition, the coupling law of stress development and thermal deformation of the support chord and cable caused by the antenna structure constraint position and other parameters is analyzed. In a uniform thermal field, the thermal stress of cables in the central module of the structure is the highest and that of the chord components in the same-circle modules is essentially the same. The thermally stress of the upper chords increases progressively toward the outer module, whereas that of cables decreases in the same direction. The thermal deformation at the upper-layer centroid of the structure can reach about 15 mm, so the influence on the accuracy of the antenna cannot be ignored. When the splicing vertical rod of adjacent modules in the outermost of the support structure is taken as the constraint connecting with the extension arm, the thermal deformation of the structure is minimum. The heat-insulating composite coating should be adopted on the surface of the antenna structure to reduce the thermal deformation and improve the adaptability. The thermal-structural analysis model proposed in this study could accurately estimate the behaviour of thermal deformation for the modular space deployable antenna, but the further coupling condition of the nonuniform temperature field could still be conducted. The results can provide a reference for the basic theory and engineering application of thermal-structural analysis for extralarge-aperture modular deployable antennas in the future.