Residential buildings with heat pumps show promising possibilities for demand-side management. The operation optimization of such heating systems can lead to cost reduction and, at the same time, change the electricity consumption, which is especially prevalent in the case of a variable price signal. In this work, we will deal with the following question: How does the volatility of a variable retail electricity price change the energy consumption of buildings with a smart energy management system? In this context, we also aggregate the findings of individual households to the national level of the Austrian single-family house stock. We show that the Austrian SFH buildings stock could shift 17.7 GWh of electricity per year using a real-time electricity price from 2019. To show how the potential could develop in the future, we create three additional price signals for 2030, which differ only in their volatility. Increasing price volatility effectively incentivizes buildings to shift electric loads by pre-heating the building mass. The results show that with a quadrupling of CO2 prices, which leads to higher electricity price volatility, electricity shifted through the thermal mass of buildings increases by 59.6%. However, the cost reductions for single households are not big enough to trigger an additional investment into a smart energy management system.