Thermal error compensation via a numeric control (NC) system is a proven option for upgrading the precision of existing machine tools. The main advantage is the generally cost-effective application, as no changes to the machine design are necessary. Since many modern machine tools are equipped with standard numeric controls along with additional functions and integrated temperature sensors in the machine, compensation methods such as a characteristic diagram (CD) based compensation can be implemented. To increase the applicability and reliability of this CD regression method, a hybrid model approach with a virtual thermo-elastic finite element (FE) machine model and a real-time computable structural model of a machine tool was developed. The structural model uses model order reduction to calculate the current load case in real-time using continuously recorded machine data (motor current, axis position, temperatures). It acts as a virtual monitoring application to check, whether the current machine condition still matches the current CD based prediction. If the current load case is not suitable to the active CDs or any other stored CDs, the generation of new CDs is automatically triggered. In this process, the thermal boundary conditions for the FE simulation are generated for that respective load case and CDs are calculated to replace the active ones in the NC. In this article, the integration of the hybrid compensation method using an FE model and a structural model of a machine tool is methodically demonstrated. The main focus is on the integration of different software and hardware architectures and their interaction.