The world's largest cities under climate change and their adaptive capacity to rising heat.

We quantify future urban heat exposure and adaptation capacity for the 1563 largest global cities, for the first time globally integrating climate projections, urban morphology, and economic capacity. We use high-resolution mean annual temperature (MAT) projections under SSP1-2.6, SSP3-7.0, and SSP5-8.5. These are combined with Local Climate Zone (LCZ) profiles and downscaled socioeconomic data, evaluated consistently within morphological city boundaries. With this framework, we identify cities projected to exceed a 29 °C MAT threshold by 2071-2100. The number of threshold-exceeding cities is projected to rise from 17 (2011-2040) to 217 (2071-2100), exposing up to 320 million residents. Cities with compact built-up forms show higher exposure, while responsiveness to eight expert-curated adaptation measures (e.g., reflective materials, greening, water bodies) and GDP distributions reveal large regional disparities in adaptive capacity. European cities face the steepest relative warming (median + 4 °C under SSP5-8.5), while African and South American cities, despite smaller increases (+2.7 to 3.2  °C), confront higher baseline heat. Our framework demonstrates how morphology- and economy-informed adaptation planning can spatially target measures to safeguard urban habitability in a warming world.