Person re-identification (ReID) is a critical task in intelligent surveillance and security systems, often challenged by variations in pose, occlusions, and missing structural details. Existing approaches primarily rely on single-frame feature extraction, limiting their ability to handle dynamic motion patterns and environmental changes. To address these challenges, we propose a multi-modal and temporal-aware person re-identification (MTReID) algorithm for LiDAR-based surveillance. MTReID integrates Cross-Modal Self-Supervised Learning (CM-SSL) and Temporal Trajectory-Aware Embedding (TTAE) modules. Firstly, we design the CM-SSL to enhance feature learning by leveraging complementary modality supervision and to improve representation consistency across different conditions. In addition, by incorporating Transformer and graph neural networks, we propose the TTAE module to capture temporal dependencies, enabling robust identity matching under pose variations and movement dynamics. Experiments on benchmark datasets demonstrate that MTReID achieves significantly outperforming state-of-the-art methods.