The study carried out by simulation, concerns the thermal behavior of an office building’s solar fresh air cooling system, based on a LiBr-H2O absorption chiller in different climatic conditions. The coefficient of performance (COP) and the solar fraction were considered performance parameters and were analyzed with respect to the operating limits—the risk of crystallization and maintaining at least a minimum degassing zone. A new correlation between the required solar hot temperature and the cooling water temperature was established and then embedded in another new correlation between the COP and the cooling water temperature that was used in simulations during the whole cooling season corresponding to each location. It was found that—the solar hot water should be maintained in the range of (80–100) °C depending on the cooling water temperature, the COP of the solar LiBr-H2O absorption chiller with or without cold storage tank could reach (76.5–82.4)% depending on the location, and the solar fraction could reach (29.5–62.0)% without cold storage tank and could exceed 100% with cold storage tank, and the excess cooling power being available to cover other types of cooling loads—through the building envelope, from lighting, and from occupants, etc.