Heat pumps are an alternative solution to conventional gas heating systems, and the demand for them has increased by over 30% this year in Austria. At the same time, electricity prices rise and increasing volatile renewable production makes load shifting with heat pumps more attractive. Optimization algorithms often determine when to shift loads with heat pumps. However, these optimizations are usually computationally expensive, so reduced-order models are popularly used. This paper will answer the question to what extent an optimization for a heat pump-operated building based on a reduced-order model is suitable to minimize operation costs. We use two different models for the same buildings to answer this question. The first model calculates the heating demand based on a reduced-order model and optimizes heat pump operation, keeping the indoor temperature in between a specific bandwidth. A non-linear building simulation model uses the resulting indoor temperature as set temperature. By comparing the results of the complex building simulation model with the optimized set temperature from the reduced-order model to a reference scenario, we determine how effective the optimization was. The building thermodynamics depend highly on building parameters like insulation, thermal mass, and the heating system. Results will show to which extent the reduced-order model sufficiently predicts heating demand for different types of heating systems, in particular for conventional, high-temperature radiators and large surface heating systems or thermal building activation.