Thermal errors remain the most difficult type of manufacturing inaccuracy of cutting machine tools due to the challenges in predicting or avoiding them. Thermal compensation using joined submodels for all relevant machine subassemblies reduces the complexity for all submodels because they handle smaller, simpler geometries and less heat sources/sinks. Model training can be done using simulations, where the thermal errors of each subassembly can be computed. With enough training data, simple regression models suffice to predict the thermal error at the subassembly level. This method is demonstrated on a machine tool and validated using measurement data. The main drawbacks of the geometric compensation method are that it is difficult to train and optimize the subassembly models from measurement data of a specific machine. To solve this issue, the residual error is predicted with adaptive learning control using ARX models, which are trained from thermal measurements and enable the overall model to overcome differences between simulation and real machine. They also allow the model to adapt to changing thermal conditions and untrained thermal load cases, thereby increasing the overall accuracy and robustness significantly. This showed a reduction of the volumetric root mean square error from 44 to 7 µm. One final issue is the integration of thermal compensation models into the machine tool control. The paper describes different methods of realizing the control integration and challenges of obtaining real-time thermal position offsets.