The transition to a renewable heating system poses extraordinary policy challenges to societies in Europe and beyond. Many buildings are heated decentrally, which makes broad public acceptance essential. As governments may be held responsible for perceived policy impacts on individuals, analyzing their effects on electoral support is of high relevance. This study examines the electoral impact of an amendment to the German Buildings Energy Act which proposed a phase-out of fossil-fueled heating systems. We combine municipal election data with granular socioeconomic and building stock data and apply difference-in-differences regressions to identify treatment effects of the policy amendment on electoral support. We find that material costs of the policy, proxied by the characteristics of the local building stock, led to relative gains for the right-wing populist party, further increasing in low-income areas. These findings highlight the importance of holistic climate policy approaches that account for heterogeneous burdens and counteract a political backlash through compensation policies.