The two-component heating system consists of a combination of air-based floor heating and direct air heating, with ventilation and extraction and heat recovery. The direct airflow consists exclusively of heated outside air, the amount corresponding to the building's external air intake requirement. The control system comprises a two-step sequential control of the air throughput of the direct air heating system and of the air distribution for the floor heating airflow. A special heating switch makes it possible to switch off the direct air heating system separately, and to select rapid warm-up. The way in which the new heating system works has been tested in a pilot set-up and proven by comprehensive measurements. In addition, a simulation model was produced which gave substantial confirmation of the measurements. (orig.) With 9 refs., 37 tabs., 63 figs.