The backless cable-stayed bridge has the advantages of beautiful shape and reasonable force, but due to the low overall stiffness of the bridge pylon during cantilever construction, it is susceptible to the effect of solar temperature. To reveal the temperature deformation laws and achieve accurate alignment prediction during the installation process of steel–concrete composite pylons in complex environments, a refined numerical simulation model for the 3D bridge temperature field was established based on the proposed automatic sunshine-shadow recognition method. Subsequently, the optimal time periods for construction control are provided. The results of the study show that, during the cantilever construction of the bridge pylon, one pylon column will shade the other pylon column, resulting in asynchronous deformation that can reach 7.6 mm. The effect of solar temperature on the displacement of the bridge pylon is significant, where the maximum daily change in transverse displacement in the cantilevered state of the pylon can reach 33.6 mm, and the maximum change in cable force value can reach 52 kN. In order to mitigate the effect of solar radiation, the best construction time for the bridge pylon is 19:30~9:30, while the tensioning and measurement of the cable should be avoided from 6:00~18:00. This strategy ensures that the control of the pylon top displacement is maintained within 1/4000 of the pylon height, and the error in cable force is kept within 5%.