Distributive energy justice is measured by the degree to which, and whether, different members of society have equal share in the benefits and burdens of the energy system. One way to achieve distributional energy justice is to ensure all households, regardless of income, can use as much energy as they need to heat and cool their home to desired temperature. We define a household's cooling balance point (CBP) as the ideal set temperature at which the household desires to keep its living space in summer; the heating balance point (HBP) is defined as the ideal set temperature in winter. To quantify the extent to which balance points were disproportionately concentrated among certain income groups, we used the extended concentration index. This index has an inequality aversion parameter that reflects the value judgment of a society. If this parameter <1, the society is pro-rich; if this parameter >1, as it increases, the society becomes more pro-poor. We estimated the empirical value of the income-related inequality aversion in eight U.S. states and examined several effects of demographic characteristics on inequality aversion.In an online survey, 1066 (from four southern states) and 906 (from four Midwest states) participants made choices between energy policies leading to different distributions of CBP (southern) or HBP (Midwest) across five income groups in a hypothetical society. Participants showed a pro-poor propensity: the median inequality aversions were 1.37, 95% CI of [1.35, 1.39] (CBP) and 1.56, 95% CI of [1.56, 1.60] (HBP). For both CBP and HBP: younger participants were less averse to inequality. For CBP, blacks (vs. whites) and conservatives (vs. centrist) were less averse to inequality; for HBP, Hispanics (vs. whites), low (vs. high) education participants, and those whose homes were well insulated (vs. adequately and vs. poorly insulated) were less averse to inequality. Our findings provide insights into how the broader public values energy justice, which further provides important policymaking implications.