This study explores the application of Model Predictive Control (MPC) in the heating system of a one-zone building as a strategy for achieving better temperature comfort and more efficient operation of the heating system compared to traditional control methods. The primary advantage of MPC lies in its ability to integrate weather predictions, future demand trends and operational constraints into the optimisation process. The predictive control approach is based on a simplified grey box mathematical model proposed to capture the thermal dynamics of the building effectively. This is represented using first-order linear differential equations arranged into a state-space model. Thermal model parameters are calibrated offline using data from DesignBuilder simulations to ensure accuracy. The MPC strategy optimises input sequences by minimising a predefined objective function at 15-min intervals, balancing temperature comfort and energy efficiency constraints. The performance of the proposed controller is validated through co-simulation using EnergyPlus and Matlab, with a case study of a single-zone building in Hungary. The controlled input variable is the heat emitted by an electric underfloor heating system, while external disturbances include occupancy, other heat sources, and weather conditions. The study assesses the performance of the controller over several days with different weather characteristics—overcast, clear-sky, and extremely cold conditions—as well as the entire heating season. Results show that MPC control improves temperature reference tracking accuracy by 50% over a heating season, provides better temperature comfort and significantly decreases peak energy demand compared to a rule-based controller.