Energy poverty is a key dimension of multidimensional poverty and a major challenge for climate action. This study examines how climate policies affect energy poverty, especially the role of carbon tax revenue recycling in coordinating climate mitigation and energy poverty alleviation. Using an integrated Climate-Economy-Energy Poverty (RICE-EP) model that incorporates inequality aspects of energy poverty, the study analyzes the effects of climate policies on household energy consumption. The study simulates various scenarios of climate actions and carbon tax revenue recycling and finds that: i) Carbon tax revenue recycling can simultaneously advance climate change mitigation and energy poverty reduction goals, it can promote climate mitigation and enhance equity by lowering the abatement costs borne by low-income populations; ii) However, the interactions between stringent climate targets and energy affordability are complex. Modeling suggests that even optimal revenue recycling fails to prevent exacerbated energy poverty among disadvantaged groups under ambitious 2 °C climate targets; iii) Analysis indicates that an emissions reduction rate approaching 43 %, enabled by a carbon tax calibrated to incentivize an equitable transition, could maximize alleviation of energy poverty by directing subsidy support to low-income groups. The study methodology and findings offer valuable, actionable insights into coordinating equitable climate and economic policies.