The rapid expansion of distributed Remote Patient Monitoring (RPM) infrastructures introduces significant cybersecurity vulnerabilities, as Internet of Medical Things (IoMT) devices continuously stream sensitive physiological data across organizational boundaries. Existing centralized threat detection paradigms are poorly suited to this environment, often failing to capture the temporal evolution of attacks while violating data sovereignty requirements under Health Insurance Portability and Accountability Act of 1996 (HIPAA) and General Data Protection Regulation (GDPR). To address these challenges, we propose Federated Temporal Retrieval-Augmented Generation (FedTempRAG), a novel framework for privacy-preserving, real-time threat intelligence in distributed RPM ecosystems. FedTempRAG integrates a decentralized vector database for cross-institutional retrieval, a dynamic temporal knowledge graph to model attack progression, and a secure aggregation protocol that enables privacy-preserving collaborative learning. Our implementation adopts homomorphic encryption for secure query processing and Byzantine-resilient aggregation to defend against adversarial participants. We evaluated FedTempRAG on a simulated multi-hospital RPM network using real-world medical threat datasets and high-fidelity emulated IoMT environments derived from public RPM repositories. Experimental results demonstrate that FedTempRAG achieves 94.3% detection accuracy, 91.7% recall, and a 0.930 F1-score, while maintaining an average inference latency of 847 -ms and a 9.8% computation overhead, enabling practical real-time deployment in RPM systems. The temporal reasoning component successfully reconstructed many multi-stage attack lifecycles, highlighting the effectiveness of integrating temporal context into federated threat intelligence. These findings establish FedTempRAG as a robust foundation for next-generation RPM security, achieving a practical balance between collaborative intelligence, temporal awareness, system efficiency, and strict privacy preservation.