This article presents an original study on the impact of climate change and the area of windows Awi (factor X1), the thermal transmittance coefficient of windows Uwi (factor X2), and the coefficient of total solar transmittance factor of the glazing ggl (factor X3) on the index of annual usable energy demand for heating EUH (function Y) of a single-family residential building in the climatic conditions of Bialystok (Poland), which were loaded with an equal gradual increase in average monthly external temperature by Δθe,n (factor X4). Based on the results of the computational experiment, a deterministic mathematical model of this dependence was developed, and the effects of selected factors on the Y function were analyzed for the considered climatic conditions. Moreover, in cases of selected variants, the influence of the energy source on the amount of final energy used and CO2 emissions was studied. It was found that an increase in the average monthly external temperature reduces the EUH of the tested building by 8.4% per every 1 °C of increase in Δθe,n. The reduction in CO2 emissions as a result of climate change is visible for systems with low efficiency and high emission factors (wood boiler), while in the case of pro-ecological high-efficiency systems (with a ground-source pump heat) it is inappreciable. Due to the need to decarbonize buildings, knowledge about the impact of the properties of windows, which are the weakest element in terms of heat loss through the building envelope, as well as the type of heat source on heat demand and CO2 emissions, is very important for engineers and designers when making the correct decisions.