Temporal perception, the ability to detect and track objects over time, is critical in autonomous driving for maintaining a comprehensive understanding of dynamic environments. However, this task is hindered by significant challenges, including incomplete perception caused by occluded objects and observational blind spots, which are common in singlevehicle perception systems. To address these issues, we introduce LET-VIC, a LiDAR-based End-to-End Tracking framework for Vehicle-Infrastructure Cooperation (VIC). LET-VIC leverages Vehicle-to-Everything (V2X) communication to enhance temporal perception by fusing spatial and temporal data from both vehicle and infrastructure sensors. First, it spatially integrates Bird's Eye View (BEV) features from vehicle-side and infrastructureside LiDAR data, creating a comprehensive view that mitigates occlusions and compensates for blind spots. Second, LET-VIC incorporates temporal context across frames, allowing the model to leverage historical data for enhanced tracking stability and accuracy. To further improve robustness, LET-VIC includes a Calibration Error Compensation (CEC) module to address sensor misalignments and ensure precise feature alignment. Experiments on the V2X-Seq-SPD dataset demonstrate that LET-VIC significantly outperforms baseline models, achieving at least a 13.7% improvement in mAP and a 13.1% improvement in AMOTA without considering communication delays. This work offers a practical solution and a new research direction for advancing temporal perception in autonomous driving through vehicle-infrastructure cooperation.