With the continuous rise of industry 4.0 applications, artificial intelligence and data driven monitoring systems for machine tools proved themselves as highly capable alternatives to classical analytical approaches. However, their precision is limited to a number of crucial aspects. One of the main aspects revolves around the lack of meaningful data, which leads to imprecise and false model predictions. This issue is closely linked to production processes and machine tools in production engineering, as the available amount of meaningful real data is strongly limited. The usage of simulation models to acquire additional synthetic data is able to fill this lack. This work looks into improving the prediction accuracy of a deep learning model for temperature forecasting of a 3-axis precision machine by combing and comparing real process data with domain randomized simulation data. The used thermal simulation model is based on finite element models of the machine assemblies. Model order reduction techniques were applied to the FE models to reduce the computational effort, increasing the simulation-to-reality gap. The approach is evaluated on unseen real data, demonstrating the underlying potential of the inclusion of synthetic data from simulation models of machine behavior.