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Thermal energy storage is essential to compensate for energy peaks and troughs of renewable energy sources. However, to implement this storage in new or existing industries, robust and accurate component models are required. This work examines the development of a mechanistic grey-box model for a sensible thermal energy storage, a packed-bed regenerator. The mechanistic grey-box model consists of physical relations/equations and uses experimental data to optimize specific parameters of these equations. Using this approach, a basic model and two models with extensions I and II, which vary in their number from Equations (3) to (5) and parameters (3 to 6) to be fitted, are proposed. The three models’ results are analyzed and compared to existing models of the regenerator, a data-driven and a purely physical model. The results show that all developed grey-box models can extrapolate and approximate the physical behavior of the regenerator well. In particular, the extended model II shows excellent performance. While the existing data-driven model lacks robustness and the purely physical model lacks accuracy, the hybrid grey-box models do not show significant disadvantages. Compared to the data-driven and physical model, the grey-box models especially stands out due to their high accuracy, low computational effort, and high robustness.