This article presents the results of a numerical study investigating the influence of the main building parameters on the indoor space heating energy flexibility of a Danish house. The focus is placed here on the envelope insulation level, the structural thermal mass, the additional thermal mass of indoor content (indoor items/furniture, PCM integrated in furnishing, PCM wallboards) and the type of heating system. The heating energy flexibility is defined as the dwelling's ability to shift heating use in time without jeopardizing indoor comfort and technical constraints. A heat storage strategy with indoor temperature set point modulation controlled by a price signal is implemented in the building model. It is shown that the insulation level of the envelope is the building's characteristic with the largest effect on the heating energy flexibility. To a lesser extent, the total thermal inertia also presents a significant influence. It was also found that the presence of indoor items and furniture in the built environment can increase the building time constant and energy flexibility potential by up to 42% and 21% respectively, in the case of dwellings with low structural thermal mass. Finally, phase change materials integrated in wallboards or in furnishing elements can increase substantially the time constant and heating energy flexibility of a house.