The need to understand how a warmer climate affects the power and energy demand in cold countries is important for urban planners and policymakers. By using data from utility bills that are commonly available today, together with outdoor temperatures, it is possible to analyze historical and future power and energy demand. The scientific value of this research includes the development of a methodology to explore effects on future heat demand in the Nordic region based on a combination of historical data, building properties, and predictions of future climate. This is achieved by using an energy signature model and regression analysis. Seventy multi-family buildings in Linköping, Sweden, are investigated from 1980 to 2050. The results show that the effects from historical variations in internal heat gains (average annual increase of 1 %) on the specific energy use for space heating (SPH) is minor for the district, i.e., less than 2 % when comparing 2020 and 1980. The opposite is found for variations in outdoor temperatures, where the average specific energy use is predicted to decrease by about 25 % in 2050 compared to 1980, with the used forecast of future climate. This corresponds to a decrease from 127 kWh/(m2·year) to 93–96 kWh/(m2·year). Additionally, the maximum heating power demand of the district is predicted to decrease by about 30 %, from 4,855 kW in 1980 to 3,468 kW in 2050. In conclusion, our results demonstrate a strong effect of decreased SPH and heating power demand in residential districts due to a warmer climate.