Heat pumps play a crucial role in decarbonizing buildings, yet conventional control strategies limit their grid-supportive potential. Model Predictive Control (MPC) offers a promising alternative to optimize energy costs and grid performance, but real-world implementations remain scarce. This study demonstrates the feasibility of MPC in a low-energy, non-residential building by integrating a controller based on electricity market prices. The system, deployed on a Raspberry Pi and integrated into the building automation system, utilizes weather forecasts and a grey-box model for load prediction. A key challenge is the lack of standardized interfaces for heat pump controls, requiring custom solutions. A 7-day performance analysis compares MPC with conventional control, focusing on economic efficiency and grid support. MPC shifts heat pump operation to periods of lower electricity prices, increasing storage temperatures and reducing the average COP from 7.6 to 6.0. Despite this, energy costs decrease by 40%, lowering the electricity procurement price from 0.36 EUR to 0.12 EUR/kWh, while the Grid Support Coefficient improves by 13%. These results confirm that MPC can enhance heat pump operation with simple component models, provided the system allows flexibility and demand is predictable.