Reducing greenhouse gas emissions while adapting cities to the consequences of climate change is one of the major challenges in the current energy transition towards a nearly carbon-free built environment. A pressing concern regards the rising of global and urban temperatures, which are expected to increase demand for building cooling and hinder the achievement of decarbonisation goals also in continental climate zones. However, available studies and assessment methods still largely overlook the environmental impacts of cooling measures in future climate conditions. This study investigates the efficiency of implementing passive cooling measures (insulation, triple glazing, solar shading, solar reflectivity of façade and natural ventilation) during the renovation of a Swedish multi-family residential building. Novel indicators and an integrated assessment method are developed by combining a climate and energy model with a carbon footprint assessment to evaluate the carbon efficiency of the measures. The results comparison between a baseline case and applied passive measures for Representative Concentration Pathways RCP4.5 and RCP8.5 in 2018, 2030 and 2050 indicates that natural ventilation, triple glazing and solar shading ensure cooling demand reduction between 13% and 56% and have the lowest carbon footprint among the assessed passive strategies. Implementing a combination of all assessed measures has the largest cooling demand reduction potential but poses a trade-off in terms of carbon footprint.