Swedish multifamily housing is dominated by warm-rent apartments, where heating is included in the rent. This, together with low inequality and an extensive social security system, has been argued to protect a large part of the Swedish population from energy poverty. However, during the energy crisis of 2021–2023, energy poverty quickly rose on the public agenda. In this paper, we challenge the dominating “high-cost”-“low-income” understanding of energy poverty, and trace underlying causes rather than descriptions of what characterizes energy poor households in an attempt to learn from, and not just about, energy poverty. Based on a deductive analysis of oral histories of heating, we show that the absence of heating costs does not necessarily protect from energy poverty and that energy poverty can exist even when heating is provided through non-market institutions. Moreover, we use the Swedish case to argue for a new conceptualization of energy poverty, where rather than seeing energy poverty as being caused by high energy costs or needs, low incomes, or poor housing standards, it is a consequence of capital inequality. Thus, energy poverty should be seen as caused by the power households have over their indoor environment, and the mechanisms that distribute this power.