The objective of this study is to assess the potential of buildings to modulate the heating power and define simple control strategies to exploit the flexibility potential considering both energy and thermal comfort. Two residential buildings with different levels of insulation and air-tightness have been modelled. This wide range of thermal properties covers the global performance of the residential building stock, and does not only focus on state-of-the-art buildings. Two strategies of modulation have been investigated: heat storage (i.e. increase of set-point) and heat conservation (i.e. decrease of set-point). Additionally, the effect of the time of activation and the type of emitter (radiator or underfloor heating) has been evaluated. A better understanding of the dynamic behaviour of buildings has been achieved in this paper. Contrary to other storage solutions (e.g. battery, hot water tank), the modulation potential of the thermal mass depends on several factors (level of insulation, type of emitter, etc) and varies over time (cold vs. transition season). The autonomy of a poorly-insulated building is relatively short, whereas passive houses have a long time constant. This characteristic implies differences in the control strategy to make use of the flexibility potential without violating comfort.