Low-income residents are among the most vulnerable groups to climate change in urban areas, particularly regarding heat stress. However, their perceptions about heat and the impacts they face go often undocumented, and are seldom considered in decision-making processes delivering adaptation. This paper presents a robust tool to allow the integration of perception, concerns and impacts of different income groups in urban adaptation planning and governance, using the City of New York as a case study. Employing online interviews—a solid method to reach poorer households—and Fuzzy Cognitive Mapping, we compare impacts and adaptation perception to heat and simulate adaptation scenarios. Results reveal that lower income groups are more concerned about impacts of heat waves than middle- and high-income populations. All income groups see citizens more in charge of adaptation, although more people from the lower income groups regard it necessary to do much more to protect themselves, proportionately more people from the higher income groups think they are doing the right amount. The scenario analysis shows that, compared to investments in the water/electricity and health system, improvements in the transit system would yield the largest decrease in negative impacts during heat, benefitting all income groups jointly.