To address missing and anomalous bridge girder-end displacement data caused by sensor failures or transmission interruptions in structural health monitoring, a feature-subspace-based deep learning reconstruction framework using temperature-displacement correlation is proposed. The framework integrates singular spectrum analysis (SSA) to extract thermally induced components and reduce noise interference, adopts the mutual information criterion (MIC) to select key temperature features, and constructs a hybrid LSTM-Transformer network to capture multi-scale spatiotemporal dependencies through local recurrence and global attention mechanisms. The arithmetic optimization algorithm (AOA) is used to collaboratively optimize hyperparameters and feature-selection parameters, and a dynamic conformal inference (DCI)-based uncertainty quantification method is further introduced to provide confidence intervals for engineering decision-making. The method is applied to long-term monitoring data from the Ningbo Bund Bridge. The mean absolute errors for reconstructing the southeast (DT-1) and northwest (DT-4) girder-end displacements are 0.0850 mm and 0.0406 mm, respectively, with R2 values exceeding 0.98. The model accurately characterizes the hysteresis behavior in the temperature-displacement relationship and maintains high accuracy outside the training dataset, showing good cross-seasonal generalization capability. The framework also exhibits strong robustness under sparse monitoring conditions and can effectively handle local outliers and continuous data gaps, indicating that it can serve as a reliable and economical data reconstruction solution for bridge health monitoring under sensor failure scenarios.