Wall-mounted solar chimneys use solar radiation to heat the air inside the chimney cavity and use thermal pressure to create natural convection. Applying this principle allows for the indoor ventilation of a building without energy consumption. However, in wall-mounted solar chimney designs, different air inlet and outlet design dimensions can have varying degrees of impact on the effectiveness of wall-mounted solar chimney ventilation. In order to analyze the internal airflow state and airflow temperature field distribution of wall-mounted solar chimneys, physical models of wall-mounted solar chimneys with six different air outlet-to-inlet cross-sectional area ratios were developed in this research work. Before numerical simulation analysis, heat transfer analysis of the wall-mounted solar chimney’s structural components and airflow channels was carried out, and corresponding mathematical heat transfer models were established. The internal flow state and temperature distribution characteristics of a wall-mounted solar chimney were analyzed by steady-state simulations using the computational fluid dynamics software, Ansys Fluent. Finally, transient simulation calculation analysis was conducted under six different S-value models to investigate the variation in the natural ventilation of a single-story building’s wall-mounted solar chimney for a whole day. The study showed that under the same simulation conditions, 80% ≤ S < 100% effectively avoided the formation of vortices in the internal airflow of the wall-mounted solar chimneys and kept the ventilation effect of wall-mounted solar chimneys at a high level. The results of this study provide a reference for the optimization of research on the design of the air inlet and outlet structures of wall-mounted solar chimneys for single-story buildings.