Due to different temporal combinations of energy generation processes, the global warming potential (GWP) of energy supply evolves constantly. Despite this, the greenhouse gas (GHG) emissions related to the energy consumption in buildings are commonly assessed with yearly averaged carbon content of the energy supply. The knowledge of the hourly carbon content of the energy supply, would allow a more realistic assessment of the GHG emissions. Moreover, a temporal relationship between the GWP energy supply and building energy demand for reducing carbon footprint could be addressed. In this study, different methods to evaluate the hourly carbon contents of the on-site available energies are presented. The potential of load shifting for GHG emission mitigation is also investigated. To test the methodology, an application to a case study where the energy is supplied from the electrical grid and on-site renewables is proposed. The chosen case study is the smart living building, currently being designed and expected to be built by 2020 in Fribourg, Switzerland. This study points out significant differences between a yearly average and an hourly dynamic carbon emission assessment. Carbon footprint benefits by load shifting at day scale are found to be very limited in the context of the smart living building.