To decarbonize the heating sector, the 4th and 5th generations of district heating networks have been identified as promising solutions. They offer superior energy efficiency, economic viability, and environmental advantages compared to decentralized, individual heating systems. However, they raise several challenges concerning their design and control optimization due to their size and the operational constraints of the production systems involved such as inertial heat generators, intermittent renewable energy sources and thermal energy storage. As a result, numerical simulations of these networks are computationally heavy which makes fast optimal control a complex and challenging task. A common strategy to address this limitation is to formulate reduced order models or to establish fast and yet accurate surrogate models. In this work, we present a novel surrogate modeling framework to rapidly predict district heating networks transients. Our model is based on a physics-guided spatio-temporal convolutional graph neural network. While similar work focused mainly on the prediction of thermal loads, this paper tackles the challenge of simulating complex and non-linear behaviors of the distribution network of district heating systems. The results show that the simulation time using our model is 99% less than a physical simulator while maintaining a high accuracy. In addition, we have conducted an ablation study and a residual analysis to test the robustness of the proposed model. Furthermore, the generalization ability of our approach is assessed by evaluating it against different district heating network topologies.