This article presents the impact of climate change on air treatment processes and energy demand in a selected air-conditioning system. The analysis was performed for a system supplying rooms with pre-treated primary air. Further treatment occurred directly in the rooms with individual devices such as fan coils or chilled beams. The analysis of the second stage of air treatment was not part of this study. The calculations were made for the city of Warsaw, where, according to the climate analysis for the period 1961–2020, an increase in outside temperature by 0.4 °C per decade and an increase in air humidity by 0.2 g/kg per decade were observed. The system analysis was divided into two stages. The first, including calculations made for monthly average climate data for the entire period of 1961–2020, shows changes in the energy demand of the system, resulting from progressive climate change. This analysis confirmed the general tendency of increasing demand for cooling energy and decreasing demand for heating energy, which is also observed in many other regions of the world. The second stage, based on calculations for hourly climate data in selected years, is an analysis of the operation of all elements of the system equipment. Research has identified areas that will have an increasing impact on the energy efficiency of the whole air condition system during further climate change.