Edge data centers are expected to become prevalent providing low latency computing power for 5G mobile and IoT applications. This article develops two models for the complete cooling system of an edge data center: one model based on the laws of thermodynamics and one data-driven model based on LSTM neural networks. The models are validated against an actual edge data center experimental set-up showing root mean squared errors (RMSE) for most individual components below 1 °C over a simulation period of approximately 10 hours; which compares favourably to state-of-the-art models.