One of the major changes regarding HVAC systems in new or renovated residential buildings is the incorporation of heating in the ventilation system, providing an air heating system. In buildings equipped with air heating systems, indoor climate is commonly controlled based on a reference zone, which leads to unsatisfactory thermal condition in the other zones. In addition, this strategy is not energy-efficient for buildings due to overheating that can occur in some zones. This study presents control logic for a novel-designed demand-controlled ventilation and air heating system and develops a variable air volume (VAV) control strategy to ensure an energy-efficient operation of the system, while providing a satisfactory indoor climate conditions. The air heating system can change airflow rate and air temperature in each room quickly and accurately enabling the control of indoor climate on a room level within a dwelling. The performance of the air heating system, in terms of its effect on thermal comfort and indoor air quality in each room as well as the stability of the system has been evaluated through a full-scale laboratory experiment. The experimental result indicated the ability of the system to satisfy different temperature set-points ranging from 20 °C to 25 °C in different zones with ±0.3°C deviation from the set-points, while the system was remained stable when temperature set-points were changed in several zones during the experiment. Individual indoor air quality requirements were also satisfied with providing the required supply airflow rate to each zone, while the supply fan was running based on the critical zone reset control strategy to achieve an energy-efficient operation.