Being increasingly insulated, new buildings are more and more sensitive to variations of solar and internal gains. Due to an important use of electrical heating systems, especially in housing, France is facing a growing problem of peak load on its electricity grid. Controlling the heating system often constitutes an efficient solution to shift heating loads while maintaining indoor comfort. The proposed energy management is a predictive set of optimal commands issued from a dynamic programming optimization knowing in advance the weather, occupancy and internal gains for the next 7 days. This method is tested on a low energy house situated in France with an annual heating demand of 14 kWh/m2. In this paper, load shifting according to utility rate incentives and carbon emissions are studied. The importance of building models as well as envelope insulation and thermal mass on energy management results is shown.