With the development of seismic isolation technology, the service environment of the isolated bridge is becoming increasingly complicated, and the effect of ambient temperature on the seismic performance of isolated bridge should be considered urgently. To reduce the maximum response and residual deformation of the bridge under the action of an earthquake, combining the advantages of the lead rubber bearing (LRB) and shape memory alloy (SMA), a self-resetting SMA–LRB bearing was formed. In view of the temperature sensitivity of rubber and SMA materials, based on a 4–span SMA–LRB seismic isolation continuous girder bridge, the nonlinear dynamic time history analysis of isolated continuous girder bridges under different ambient temperatures was performed to obtain the dynamic response of the key parts of the structure, while the mechanical properties of SMA–LRB bearings at different ambient temperatures were considered. The results showed that the addition of SMA to LRB increased the horizontal rigidity and effectively controls the displacement response of the bearing. At the same time, the self-reset characteristic of SMA made the residual displacement control effective. As the ambient temperature decreases, the peak displacement and residual displacement of the LRB and SMA–LRB bearings would decrease, but the displacement control ability and self-reset ability of the SMA–LRB bearing would decrease compared with normal temperature. The stiffness of the bearing increased with the decrease of the ambient temperature, which caused an increment in the displacement of the top of the pier and the shear force at the bottom of the pier, and the shear force at the bottom of the lower pier was more sensitive to temperature changes. The qualitative evaluation of the influence of ambient temperature on the seismic performance of SMA–LRB isolated bridge can provide reference for the analysis and design of such bridges.