The inherently nonlinear, large-scale, and time-varying nature of district heating systems pose significant challenges from a control perspective. In this paper, we address these challenges by applying an economic MPC. Economic MPC is a dynamic real-time optimization method, enabling both optimal planning and stability of the closed-loop system. Our strategy constitutes several steps. First, we introduce a discrete-time modular framework for the district heating system, establishing its strict dissipativity with respect to a desired, potentially time-varying, equilibrium. We identify a set of meaningful objective functions for the district heating systems, preserving this property. Second, we show how strict dissipativity implies the turnpike property, which, in turn, guarantees approximate optimality, practical stability, and recursive feasibility for the EMPC closed-loop. Finally, we provide numerical simulations to demonstrate the effectiveness of our work.