Abstract-Existing unicast routing protocols like for example AODV are not suited well for wireless mesh networks as in such networks, most traffic flows between a large number of mobile nodes and a few access points with Internet connectivity. In this paper, we propose HEAT, an anycast routing protocol for this type of communication that is designed to scale to the network size and to be robust to node mobility. HEAT relies on a temperature field to route data packets towards the Internet gateways, as follows. Every node is assigned a temperature value, and packets are routed along increasing temperature values until they reach any of the Internet gateways, which are modeled as heat sources. Our major contribution is a distributed protocol to establish such temperature fields. The distinguishing feature of our protocol is that it does not require flooding of control messages. Rather, every node in the network determines its temperature considering only the temperature of its direct neighbors, which renders our protocol particularly scalable to the network size. We analyze our approach and compare its performance with AODV and OLSR through simulations with Glomosim. We use realistic mobility patterns extracted from geographical data of large Swiss cities. Our results clearly show the benefit of HEAT versus AODV and OLSR in terms of scalability to the number of nodes and robustness to node mobility. The packet delivery ratio with HEAT is more than two times higher than with AODV or OLSR in large mobile scenarios and we conclude that HEAT is a suitable routing protocol for city-wide wireless mesh networks.