Huge amount of energy resources greenhouse gas (GHG) emissions is devoted to the built environment. Therefore, an accurate assessment method of these indicators is compulsory. To take advantage of the temporal variation in the primary energy use and associated GHG emissions of the energy supply, we propose two ways of integrating hourly life-cycle conversion factors in building energy systems. First, to appraise the energy system design, we developed a versatile modelling and performance assessment framework using a multi-criteria approach. The simulated performances of possible energy systems are compared, and help designers systematically choose appropriate energy production and storage systems. Second, for the operation of the building, we propose an energy management procedure (EMP) that always feeds in the energy source with the least global warming potential (GWP). These two developments are tested on a case study consisting in an architectural project that should respect the 2000 W society targets. The running conditions of several energy systems are simulated and compared. The most promising scenario is identified. Compared to traditional methods, the assessment framework has a promising future but the GWP-based energy management procedure offers, in the context of the case study, limited GHG emissions mitigation at very high primary energy cost.