The establishment of temperature-displacement correlation is essential for the displacement-based performance evaluation of long-span bridges. We propose a new method based on long short-term memory (LSTM) neural network for modeling multiple temperature-displacement correlation. The LSTM neural network, which can describe the time-lag effect and is suitable for processing ultralong data sequences, is adopted as the basic neural network. We use the adaptive moment estimation method to optimize the LSTM neural network, and introduce the dropout regularization technique to improve the generalization ability of the model. The predominant thermal variables that affect the vertical displacement in the main girder of the bridge are extracted using long-term synchronous monitoring data of temperatures and displacements obtained from a three-span continuous tied arch bridge. An LSTM neural network between multiple temperature variables and displacements is established. A back propagation (BP) neural network is also modeled for comparison. The results show that the structural effective temperature has a significant nonlinear relationship with the vertical displacement in the main girder, while the temperature difference among structural components and the temperature gradient in the main arch rib have a linear correlation with the vertical displacement in the main girder. The effective temperature in the main arch rib and the temperature difference between the main girder and the main arch rib are the predominant thermal variables that result in the vertical displacement in the main girder. Compared with the BP neural network model, the LSTM neural network model proposed in this paper can dramatically reduce the reproduction error and prediction error of the thermal displacement.