The mechanical system of a cable-stayed bridge with a steel arch tower is different from that of a traditional cable-stayed bridge. In order to investigate the effects of ambient temperature variations on the main components of a cable-stayed bridge with a tower in an abnormal shape, an actual cable-stayed bridge with a steel arch tower has been used as the engineering prototype. The online temperature data of the onsite environment and the bridge components were first collected and used to analyze the time-varying effects of the environmental temperature on the cable forces, the tower obliquity and the stress of the main girder. Subsequently, the analysis was focused on the cable forces. The temperature variation simulation was applied to the finite element model of the bridge, and the temperature coupling effects caused by the temperature difference between different bridge components on the cable forces were analyzed. Lastly, the temperatures of the environment, the tower and the main girder were used as the inputs, while the cable forces were defined as the outputs of a long short-term memory neural network. The network was trained using the actual measurement samples of the temperatures and the cable forces. Data compression and feature extraction were realized during the training process. Then, the prediction model for the cable forces was established, and new temperature monitoring data were input into the network model for predicting the cable forces. The analysis results show that the temperature variations of the main girder and the steel arch tower follow a periodic rule and lag behind the ambient temperature. The strain variation tendency of the main girder accords well with the ambient temperature, but the latter has a time lag. The influence of the ambient temperature variation on the obliquity of the arch tower is very small without any periodic rule. A linear negative correlation is found between the cable forces and the ambient temperature. The temperature coupling effect caused by the temperature difference between different bridge components should be considered in the analysis. The long and short-term memory neural network is suitable for the data with timing characteristics. The cable force prediction model based on the neural network has high prediction accuracy, and it can be used for the real-time prediction of this bridge.