Faced with environmental challenges, district heating networks have been identified as a viable solution to decarbonize the heating sector. However, they raise various challenges regarding the optimization of their control given their size and the operational constraints of the energy systems involved. As a result, the numerical simulation of these networks is computationally heavy, which hinders near-instantaneous optimal control. In this work, we present the first brick of an optimization framework for the control of district heat networks using a surrogate model based on geometric deep learning. More precisely we trained specific architectures of Graph Neural Networks to emulate a thermo-hydraulic simulator of district heating network. This statistical inference method allows us to drastically reduce simulation time by 1 to 4 orders of magnitude.