## 1 Introduction  
Sensor embedded systems and Wireless Sensor Networks (WSN) have attracted many researchers from academia and industry in the recent years. WSN allow many useful applications like environmental and biological monitoring [1], military surveillance [2] and infrastructure protection [3]. Usually, sensor networks are deployed for long-term monitoring, likely at the places where the exchange of the power source (battery) might not be possible and/or this replacement is very costly (e.g., underwater monitoring, leakage of harmful chemicals). Therefore, for majority of the WSN applications, data rate and delay are commonly not so important factors in the sensor networks as energy consumption and reliability. Wireless sensor networks offer effective solutions also for vehicular sensing systems, monitoring of animal habitat and human probe systems. These applications have one common characteristic, that is mobility of sensor nodes. While vehicular systems might have sufficient resource of energy, animals (or humans) are often equipped with small monitoring tags with tiny batteries. In this paper, we would like to focus on animal and human mass monitoring applications. One typical example of such application is monitoring of habitat in certain area like forest, national park or reservation. Depending on the information we want to periodically monitor, the frequency of data generation might vary. For behavior-related data, the data generation frequency is lower than for health-related information such as heart beat. Another very useful usage of sensors is human's health status monitoring during mass events like concerts, large open air festivals or religious pilgrimages. In such applications, it might be impractical (e.g., during some event) and sometimes dangerous (e.g., wildlife habitat) to change battery. A dissipated sensor node does not mean only lost of some data, but might endanger animal (human) ending by lost or death of such animal (human) or other animals. Therefore, one of the primary goals is maximizing lifetime of every node. This is in contrary with many area monitoring applications where nodes are dropped and some redundant nodes, which are sensing overlapping area, might be used for data forwarding and dissipate earlier in order to save energy of other sensor nodes located in the more important area. In habitat monitoring, every sensor node usually has the same importance in terms of lifetime, because it is monitoring a living object. Another very important aspect of this application is mobility of the sensor nodes. As animals (humans) are moving within possibly large area, it is important to reflect to the dynamicity of the network to minimize the impact on the delivery of data to the sinks. When monitoring medical or body related data, it is likely that any significant change in data should be immediately followed by reaction (e.g., medical assistance). This wireless sensor network is also relatively sensitive to end-to-end message delay between sensor node and sink. In this paper, we propose novel data collection method which inherits the distributed and scalable nature of thermal fields and temperature transfer. The following is the summary of the key contributions:  
* To the best of our knowledge, this is the first data collection method designed for mobile sensor networks based on the theory of thermal fields. In detail, we propose creation of directed acyclic graph based on the temperature, a virtual metric, which is derived from the theory of thermal fields. Then, we design lightweight proactive communication protocol for data collection, which enables forwarding data according to the warmest path. * By using proposed algorithm we show that directed acyclic graph can be easily adapted to characteristics of node, such as energy or transmission power. We also adapt conductivity to the residual energy of the sensor node and propose Temperature exchange based Energy Adaptive Routing (TEAR) protocol for Mobile Sensor Networks (MSN).