A substantial share of the building sector in global energy demand has attracted scholars to focus on the energy efficiency of the building sector. The building’s energy consumption has been projected to increase due to mass urbanization, high living comfort standards, and, more importantly, climate change. While climate change has potential impacts on the rate of energy consumption in buildings, several studies have shown that these impacts differ from one region to another. In response, this paper aimed to investigate the impact of climate change on the heating and cooling energy demands of buildings as influential variables in building energy consumption in the city of Poznan, Poland. In this sense, through the statistical downscaling method and considering the most recent Typical Meteorological Year (2004–2018) as the baseline, the future weather data for 2050 and 2080 of the city of Poznan were produced according to the HadCM3 and A2 GHG scenario. These generated files were then used to simulate the energy demands in 16 building prototypes of the ASHRAE 90.1 standard. The results indicate an average increase in cooling load and a decrease in heating load at 135% and 40%, respectively, by 2080. Due to the higher share of heating load, the total thermal load of the buildings decreased within the study period. Therefore, while the total thermal load is currently under the decrease, to avoid its rise in the future, serious measures should be taken to control the increased cooling demand and, consequently, thermal load and GHG emissions.