The DSF (double-skin facade) system is an important element in building design and is used in adjacent spaces to control the inlet solar radiation, heat the air, reduce energy consumption, decrease the acoustics levels, and produce photovoltaic energy, among other improvements. The DSF system can, for example, be used in winter conditions to heat the air, which is then transported to non-adjacent spaces to improve the thermal comfort level and the indoor air quality that the occupants are subjected to. Smooth DSF systems, which are a focus in the literature, are subjected to higher solar radiation levels at a specific hour of the day. The semi-circular DSF system used in this work, which was built from a group of smooth DSF systems with different orientations, guarantees the reception of the highest incident solar radiation throughout the entire day. This work presents a numerical study of a new DSF system, called the semi-circular DSF. The DSF system consists of a set of 25 smooth DSFs with different orientations, each one consisting of an outer glazed surface and an inner surface provided by the outer facade of the auditorium, both separated by an air channel. In this work, the influence of the radius of the semi-circular DSF system and the opening angle of the DSF system on the thermal response of the auditorium was analysed. Thus, six auditoriums were considered: two sets of three auditoriums with radii of 5 m and 15 m, with each of the auditoriums having a different DSF opening angle (45°, 90°, and 180°). It was found that the greater the radius of the semi-circular DSF and the opening angle of the DSF system, the greater the area of its glazed surface and, consequently, the greater the availability of solar heating power. Therefore, during the occupation period, only the set of auditoriums with the largest semi-circular DSF radius managed to present acceptable levels of thermal comfort, which were verified from mid-morning until late afternoon. As for the opening angle of the DSF system, the influence was not very significant, although slight improvements in thermal comfort were noted when the value of this angle was reduced (see Case F as an example) due to the corresponding decrease in the volume of indoor air to be heated. In all auditoriums (see Case A to Case F), it was verified that the indoor air quality was acceptable for the occupants, so the airflow rate was adequately promoted by the ventilation system.