The steel box arch bridge in this study will be subjected to various temperature effects from the construction to the operation stage, including the cement hydration heat effect and the sunshine temperature effect caused by an ambient temperature change. Therefore, it is very important to control the temperature effect of steel box arch bridges. In this study, the newly built Dafeng River Bridge is selected as the steel box arch bridge. This study aims to investigate the temperature effect including hydration heat and the sunshine temperature effect of the construction process of a rigid frame-tied steel box arch bridge. The manuscript presents that the heat dissipation performance of concrete decreases with the increase in the thickness of a mass concrete structure. The average maximum temperature values of layer No. 3 are about 1.3, 1.2, and 1.1 times the average maximum temperature value of layer No. 1 for the mass concrete of the cushion cap, main pier and arch abutment, respectively. The higher the molding temperature is, the higher the maximum temperature by the hydration heat effect is. With each 5 °C increase in the molding temperature, the maximum temperature at the core area increases by about 4~5 °C for the mass concrete. The pipe cooling method is conducive to the hydration heat control effect of mass concrete. Based on the monitored temperature change and displacement change, the influences of daily temperature change on the steel lattice beam and arch rib are analyzed. A temperature rise will cause the structure to have a certain camber in the longitudinal direction, and the longitudinal or transverse displacement caused by the sunshine temperature change is no less than the vertical displacement. Due to the symmetrical construction on both sides of the river, the arch rib deformation on both sides presents symmetrical synchronous changes. Based on 84 h of continuous temperature monitoring on-site, the changing trends of the arch back temperature and ambient temperature are consistent and their difference is small during 1:00~4:00 in the morning, which is determined as the appropriate closure time for the newly built Dafeng River Bridge.