In Mediterranean regions, characterized by a hot and humid climate during summer, the exposure of facades and the position of opening windows are important parameters to enhance passive cooling in the building using buoyancy-driven airflow. An example is the double skin façade which is directly exposed to solar radiation. This approach may be present in many residential buildings and is commonly called a “solar chimney”. Often this solution collides with architectural requirements, primarily when the building is not in a favorable condition in terms of exposure to the south. The purpose of the present study is to numerically investigate the performance of an alternative type of solar chimney which is integrated into the frame of a residential building and heated from below by a horizontal plate that acts as a thermal storage. The main result observed from the simulations is an improvement of natural ventilation to the space, for different outdoor conditions, along with a saving of energy required for cooling.