Fatigue and distracted driving are among the leading causes of traffic accidents, highlighting the importance of developing efficient and non-intrusive driver monitoring systems. Traditional camera-based methods are often limited by lighting variations, occlusions, and privacy concerns. In contrast, millimeter-wave (mmWave) radar offers a non-contact, privacy-preserving, and environment-robust solution, providing a forward-looking alternative. This study introduces a novel deep learning model, RTSFN (radar-based temporal-spatial fusion network), which simultaneously analyzes the temporal motion changes and spatial posture features of the driver. RTSFN incorporates a cross-gated fusion mechanism that dynamically integrates multi-modal information, enhancing feature complementarity and stabilizing behavior recognition. Experimental results show that RTSFN effectively detects dangerous driving states with an average F1 score of 94% and recognizes specific high-risk behaviors with an average F1 score of 97% and can run in real-time on edge devices such as the NVIDIA Jetson Orin Nano, demonstrating its strong potential for deployment in intelligent transportation and in-vehicle safety systems.