The deployable Astromesh antenna has been extensively used in communication satellites in recent decades. The antenna may have large deformations and even thermal-induced vibrations under solar radiation shocks, which may affect the normal operation of the antenna. In this paper, the finite element theory and the Fourier thermal element method are combined to study the thermal–mechanical responses of the antenna under different unidirectional solar heat shocks. In addition, the reflector’s light shading effect and cable pretension is included in the thermal–mechanical coupling analysis model. The cable pretension is determined through the cable net form-finding method. The thermal–mechanical coupling analysis model is validated by two designed numerical examples using the finite element software COMSOL. Modal analyses have been conducted to further validate the accuracy of the established model and frequency sensitivity analyses are also performed. Thermal–mechanical coupling performances including the temperature distributions and thermal deformations of the Astromesh antenna under different unidirectional solar heat flux shocks are then evaluated using the established model. On this basis, effects of some key structural parameters and the reflector’s light shading effect on temperature and deformation of the Astromesh antenna are also examined. It is shown that the light shading effect of the reflector exacerbates the temperature gradient and thermal deformation of the antenna, but the antenna hardly undergoes the phenomenon of thermally excited vibration with enough cable pretension.