Deterministic global optimization of process flowsheets has so far mostly been limited to simplified thermodynamic models. Herein, we demonstrate a way to integrate accurate thermodynamic models for the optimal process design of an organic Rankine cycle (ORC) via the use of artificial neural networks (ANNs). We generate training data using the thermodynamic library Coolprop and learn thermodynamic properties. The ANNs are subsequently embedded in the process design optimization problem in a reduced-space, which is solved to global optimality using our in-house optimization software MAiNGO. The importance of accurate thermodynamics is illustrated for the design of an ORC for geothermal power generation. We show that the use of an accurate thermodynamic model leads to different design decisions in comparison to a simplified model. Furthermore, we investigate the influence of the network architecture and complexity on accuracy, optimization results and computational performance.