Swedish buildings are well insulated for winter climate, but often not optimized for summer, leading to risks of overheating during heat extremes (including heat waves). Along with a warmer climate, the risks of overheating and need for cooling are expected to increase. In this study, present and future intensity, frequency and length of overheating, based on the newly implemented recommendations for indoor temperature from the Swedish Public Health Agency, is assessed for a typical Swedish multi-story residential building in Gothenburg, Sweden. Overheating is simulated for different floor levels and room orientations using the IDA-ICE building performance simulation software. The present climate (2008–2020) is represented by observed meteorological data and the future climate (2071–2100) by statistically downscaling the observations based on RCP4.5 simulations from the EURO-CORDEX project. Furthermore, the shading effect of trees at varying distances from the building is explored. Results show that overheating occurs during heat extremes from April to October, with the highest frequency in July. Overheating periods are projected to become more intense, more frequent and longer by the end of the century. During heat waves, overheating occurs throughout the day and may last for weeks, potentially impacting not only risk groups but also the general population. The risk of overheating increases with floor level and is largest for rooms facing west and south with large windows. Trees close to buildings considerably reduce overheating in the present as well as in the future warmer climate, highlighting their effective passive cooling potential during heat extremes. The results, which are considered applicable to a large part of the building stock in Sweden as well as in other countries with similar climate and building practices, highlight the present and future challenges with overheating and the potential of trees for mitigating overheating and reducing the cooling demand in buildings.