In the coming years, an increased share of renewable energy sources (RES) is expected in the grid, bringing up the challenge of variability and fluctuation in the energy supply. The building thermal mass could be used as a storage solution to optimise the use of fluctuating energy sources. The objective of this study is thus to define how long the activation can last without compromising the comfort of users. Using Building Energy Simulation (BES) tools, the potential of three residential buildings with different levels of insulation and air-tightness has been assessed. A price signal (i.e French spot market price) has been used as an indicator of the availability of electricity. During the time of high-price, the set-point decreases, whereas the set-point increases during time of low price. Different periods of modulations have been tested: 30 minutes, 1, 2, 4, 6, 12 and 24 hour(s). The time constants of the buildings differ much depending on the level of insulation. This characteristic implies differences in the control strategy in order to make use of the flexibility potential without compromising comfort. The maximum time of activation varies from a couple of hours for a poorly-insulated building, up to 24 hours for a well-insulated building. From the grid perspective, a high flexibility potential has been observed: it is possible to move the heating need from hours with a high spot price to hours with a low spot price. Additionally, a sensitivity study has been conducted to observe the influence of the comfort criteria, the weather and the availability of electricity.