Federated learning (FL) has gained widespread adoption in Internet of Things (IoT) applications, promoting the evolution of IoT towards artificial intelligence of Things (AIoT). However, IoT devices are still vulnerable to various privacy inference attacks in FL. While current solutions aim to protect the privacy of devices during model training, the published model is still at risk from external privacy attacks during model deployment. To address the privacy concerns throughout the entire FL lifecycle, this paper proposes a privacy-enhanced and efficient federated knowledge transfer framework for IoT, named PEFKT, which integrates the knowledge transfer method and local differential privacy (LDP) mechanism. In PEFKT, we devise a data diversity-driven grouping strategy to tackle the non-independent and identically distributed (non-IID) issue in IoT. Additionally, we design a quality-aware soft-label aggregation algorithm to facilitate effective knowledge transfer, thereby improving the performance of the student model. Finally, we provide rigorous privacy analysis and validate the feasibility and effectiveness of PEFKT through extensive experiments on real datasets.