As an important environmental factor, temperature has a profound impact on bridge structures, and thermal effects are a focal point in the field of long-term bridge health monitoring. The intricate thermal mechanisms between a bridge structure and its surroundings form a complex nonlinear mapping relationship between the structural temperature field and the temperature-induced effects, which is notable for its obvious time-delayed characteristics. In order to reveal the inherent time characteristics of the temperature-induced effects within a bridge and to lay the foundation for the assessment of the structural condition of a bridge based on the thermal response, this study proposes a method to model the temperature-thermal effect mapping within a bridge. By using temperature data from multiple monitoring points as inputs to reconstruct static girder end displacements and considering the time lag effect of temperature on the structural behavior, the method employs a Geometric Mean Optimizer (GMO) within the framework of a Temporal Convolutional Network (TCN). The GMO determines the optimal time lag parameters while fine-tuning the TCN hyper-parameters. The performance of the model is fully validated by the measurement data from an operational cable-stayed bridge.