Buildings are responsible for a large part of energy demand worldwide. To collaborate to reduce this demand, this paper aims to present a computational model to analyze the performance of an earth–air heat exchanger (EAHE) based on computational fluid dynamics using the ANSYS/Fluent® software in the simulations. This passive air conditioning system uses the soil as a heat exchanger, taking advantage of the fact that the temperature of the soil at a certain depth remains relatively constant, regardless of the weather conditions above the surface, promoting heating, cooling, or ventilation for buildings. The air temperature values obtained were compared with experimental data from sensors installed in an EAHE at the Federal University of Technology—Parana, Ponta Grossa/Brazil (25.1° South, 50.16° West) to validate the computational model. A high computational effort would be demanded to perform these simulations involving the whole soil domain and the climatic boundary conditions. In order to optimize the numerical analysis of EAHE, two reduced models for the soil and heat exchanger domains were verified. First, a constant temperature of 23.7 °C was imposed on the surface of the exchanger tube, corresponding to the average soil temperature at a depth of 1.5 m. Afterward, a reduced soil domain extending 0.5 m in all directions from the heat exchanger serpentine was considered. Likewise, constant temperatures were imposed on the upper and lower surfaces of the soil domain, also obtained experimentally. In both cases, the temperature values obtained through the fast simulations showed good agreement compared to the experimental values. Barely explored in the literature, the thermal behavior of the two identical indoor environments at the university was also compared, in which the climatized environment, with the EAHE working in a closed loop, obtained milder and smaller amplitude air temperatures.