Efficient and accurate grey-box building models, including water-based heating and cooling systems, are crucial for simulating and optimizing the energy demand of building, neighborhood, and network scenarios. However, the numerical effort and the amount of input data required for existing models are still high, and the parameterization of these systems is very labor-intensive. This paper presents a grey-box model that addresses these limitations by requiring minimal input data and offering a highly efficient parameterization method. Using physical principles, the model was validated against a detailed physical building model and measurement data. Our results show that the grey-box model accurately predicts return temperatures (σ = 0.37 K, µ = 0.05 K) and room air temperatures (σ = 0.62 K, µ = 0.28 K). Compared to 8229 s for the detailed physical model, the model requires only 18 s for a one-year simulation. The model also shows robust behavior with alternative weather data and control strategies. The key contribution of this work is the development of a grey-box model that combines high accuracy and numerical efficiency with significantly reduced data and parameterization requirements, with possible applications in large-scale building simulations, demand-side management, short-term energy storage strategies, and model predictive control.