Spiking global energy prices make it all the more important to understand the distributional effects of commonly used energy transition policies such as financially-based demand management. We examine how building energy efficiency impacts the effect of time-of-use rates; peak prices could differently affect curtailment behaviour and bills in homes that require more continual energy use for comfort. Using a sample of 3,145 households in the Australian Capital Territory with panel data for up to five years, we use two-way fixed effects to estimate the effect of switching to a time-of-use (TOU) rate on household electricity use and bills, allowing for heterogeneous effects as a function of building Energy Efficiency Rating (EER). Analyses indicate that low-EER households dependent on electricity for heating curtail use when on TOU rates, while high-EER households do not. This does not appear to financially disadvantage low-EER households, but may impact comfort. Our findings suggest that the household responses to TOU rates can differ as a function of building energy efficiency for those households that are reliant on electricity for heating. This has implications for TOU rate design and demand management policies, particularly in the context of policies for electrification.