One of the most important requirements for a routing protocol in wireless body area networks (WBANs) is to lower the network's temperature increase. The temperature of a node is closely related to its activities. The proactive routing approach, which is used by existing routing protocols for WBANs, tends to produce a higher temperature increase due to more frequent activities, compared to the on-demand reactive routing approach. In this paper, therefore, we propose a reactive routing protocol for WBANs called priority-based temperature-aware routing (PTR). In addition to lowering the temperature increase, the protocol also recognizes vital nodes and prioritizes them so they are able to achieve higher throughput. Simulation results show that the PTR protocol achieves a 50% lower temperature increase compared to the conventional temperature-aware routing protocol and is able to improve throughput of vital nodes by 35% when the priority mode is enabled.