Improved energy efficiency in the housing stock is an important undertaking in the energy transition but is associated with both opportunities and risks. While there are possibilities to reduce energy inequalities in the housing stock, inequalities also risk being aggravated as actions for energy efficiency usually aim at the least energy efficient - and thus sometimes the least privileged - parts of the housing stock. In this paper, we use two different energy performance metrics (kWh/m2 and kWh/capita) to investigate the energy inequality in the Swedish multifamily building stock and explore the effects of these inequalities in the energy transition. More specifically, we investigate the implementation of individual metering and billing of energy for heating, which was recently implemented in the least energy efficient part of the housing stock. It was found that low-income households were overrepresented in the affected buildings. The consequence of this implementation is thus that the strongest protection against energy poverty in Sweden (collective billing for heating) is removed in a part of the housing stock where two of the predictors for energy poverty - low income and low energy performance - are overrepresented. It was concluded that acknowledging inequalities is crucial to avoid risks associated with the energy transition.