Extreme Heat Events (EHE) are a major concern for many urban areas worldwide and are considered as one of the deadliest natural hazards globally. Climate change and socioeconomic trends (exposure and susceptibility) are expected to exacerbate the risk of urban heat stress. Several urban areas have recently declared a climate emergency and initiated the adaptation process, but progress is still patchy, uncoordinated, and of varied quality. The main constraint is the lack of mechanisms for monitoring and reporting adaptation strategies, not allowing the supervision and evaluation of the adaptation process. The EU-funded project U-ADAPT! (Urban-Adaptation) focuses on the concrete expression of adaptation to evaluate the current implementation and effectiveness of adaptation measures and strategies to reduce Heat Disaster Risk (HDR), moving the emphasis from the study of vulnerability, resilience, and potential adaptation (adaptation capacity) of communities to the actual depth and pace of the past and current adaptation process. In this article, we discuss the theoretical support and design of the project and set the base for next project stages, which ultimately aims to create a unique interdisciplinary framework and a replicable multidimensional indicator on adaptation to EHE that empower European Union citizens to demand a safe and sustainable environment and hold institutions accountable for the adaptation process to current and upcoming risks.