<p>Energy poverty currently affects a significant number of European citizens and represents a growing problem that needs to be addressed. Although the literature on energy poverty in developed countries has focused on cold climates and heating-related deprivation, the impacts of climate change, particularly increasing temperatures, engender a novel form of vulnerability: <i>summer energy poverty</i>. This phenomenon refers to households that are unable to maintain adequate cooling in their homes during periods of elevated temperatures. The objective of this paper is to develop a multidimensional and climate-aware indicator to measure energy poverty by incorporating a direct quantification of thermal discomfort based on climatic variables. Thermal discomfort refers to experiencing indoor temperatures that fall outside an acceptable comfort range, potentially affecting health, well-being, and daily functioning. This innovative metric combines environmental variables (air temperature and humidity) with household-level data (financial resources and dwelling quality) to assess real exposure to heat or cold stress. By applying this indicator to data from tropical French overseas territories, this study reveals significant differences in identifying energy-poor households. This study also provides new perspectives for measuring and addressing energy poverty in both cold and hot climates, especially in the context of ongoing climate change.</p>