High-level assessments of climate change impacts aggregate multiple perils into a common framework. This requires incorporating multiple dimensions of uncertainty. Here we propose a methodology to transparently assess these uncertainties within the ‘Reasons for Concern’ framework, using extreme heat as a case study. We quantitatively discriminate multiple dimensions of uncertainty, including future vulnerability and exposure to changing climate hazards. High risks from extreme heat materialise after 1.5–2 °C and very high risks between 2–3.5 °C of warming. Risks emerge earlier if global assessments were based on national risk thresholds, underscoring the need for stringent mitigation to limit future extreme heat risks.