In this thesis, we develop a discrete time model of a recently proposed algorithm, inspired by thermodynamics, for message routing in Disruption Tolerant Networks (DTNs). We model the evolution of the temperature at the nodes as a stochastic switched linear system and show that the temperatures converge in distribution to a unique stationary distribution that is independent of initial conditions. The proof of this result borrows tools from Iterated Random Maps (IRMs) and Queuing theory. Lastly, we simulate the proposed algorithm, using a variety of mobility models, in order to observe the performance of the algorithm under various conditions.