The importance of air quality in indoor environments has gained significant attention due to the Coronavirus pandemic: the risk of airborne transmission of the virus has made it imperative to reconsider many aspects of building design. Among the various categories of buildings, it is crucial to pay attention to schools’ buildings. This paper presents a detailed summary of the research conducted to analyze the indoor air quality inside a kindergarten in the province of Bari. Among school buildings, kindergartens represent a particular exception because they host children aged 3–6 years, who are extremely sensitive to indoor air quality. To analyze the comfort inside the classrooms, a monitoring campaign of indoor air quality parameters was conducted in two classrooms of the school used as a sample for this investigation. The data analysis provided interesting findings regarding the classroom temperature variations, the levels of relative humidity, and users’ behavior. The temperature variations detected during the monitoring are significant and can be attributed to infiltrations due to obsolete window frames, while the levels of relative humidity do not fall within the ranges indicated by regulations for many of the monitored days. The data obtained from the temperatures and regarding ventilation were implemented within the energy model of the kindergarten; the energy model was subsequently calibrated according to the ASHRAE 14:2014 Guidelines. Starting from the size of the classroom, occupancy, and the age of the users, simulations of the accumulated CO2 levels were carried out; to perform these simulations, ventilation scenarios reflecting both summer and winter ventilation practices were hypothesized. The results demonstrate how CO2 concentrations tend to reach significantly higher levels in the winter seasons: this factor represents a problem for users’ comfort and shows the need to reconsider the design strategies of school buildings.