With the electrification of the heating sector in Europe, there is increased pressure to reduce stress to the electric grid from increased demand. Understanding the flexibility potential of the current building stock, including both efficient buildings as well as less efficient buildings, will be vital to assess the efficacy of demand-side strategies such as time-varying pricing in enabling shifts in consumer heat demand. The aim of this study is to assess the thermal flexibility potential of residential buildings with electric heating under different tariffs, and the effect of these tariffs on heating expenditure and electricity consumption. To accomplish this, a resistance–capacitance heat demand model was integrated into a linear optimization model set to find the lowest cost heating schedule for a consumer under four different tariff designs. The results indicate that time-varying tariffs can be effective in enabling shifts in the heat consumption, although the additional cost savings due to the flexibility provided by an efficient building envelope is limited (1% to 4.65% additional reduction in cost savings). The results suggest that potential flexibility is price sensitive and a function of the alignment of price and heating demand. Measures such as capacity tariffs should be considered to avoid preheating surges.