Climate change may bring new hazards through novel combinations of extreme weather (compound events)1 . Here we evaluate the possibility of dangerous heat following major tropical cyclones (TCs)—a combination with serious potential consequences given that mega-blackouts may follow powerful TCs2 , and the heavy reliance on air conditioning3 . We show that ‘TC–heat’ events are already possible along densely populated coastlines globally but, to date, only an estimated 1,000 people have been impacted. However, this number could rise markedly with over two million at risk under a storyline of the observed TCs recurring in a world 2 °C warmer than pre-industrial times. Using analogues as focusing events we show, for example, that if the catastrophic 1991 Bangladesh cyclone occurred with 2 °C global warming, there would be >70% chance of subsequent dangerous heat. This research highlights a gap in adaptation planning and a need to prepare for an emerging TC–heat compound hazard.