Federated learning aims to protect data privacy by collaboratively learning a model without sharing private data among clients. Unlike traditional parameter-based FL methods that exchange model weights or gradients during training, emerging logit-based FL approaches share model outputs (logits) on public data. This strategy promotes model heterogeneity, reduces communication overhead, and enhances clients' privacy. However, the potential privacy risks associated with these logit-based methods have been largely overlooked. This research presents the first theoretical and empirical analysis of a hidden privacy risk in logit-based FL methods - the risk that a semi-honest server (adversary) may learn clients' private models from logits. To quantify and address this threat, we develop the Adaptive Model Stealing Attack (AdaMSA) by leveraging historical logits during training. Notably, we observe that this inherent privacy risk persists even when public data is unrelated to private data, emphasizing the urgency to address privacy vulnerabilities in logit-based FL methods. Moreover, our theoretical analysis establishes the bounds of this privacy risk. We then propose a simple but effective defense strategy that perturbs the transmitted logits in the direction that minimizes the privacy risk while maximally preserving the training performance. The experimental results validate our analysis and demonstrate the effectiveness of AdaMSA and our defense strategy.