The impacts of climate change on human health are often underestimated or perceived to be in a distant future. Here, we present the projected impacts of climate change in the context of COVID-19, a recent human health catastrophe. We compared projected heat mortality with COVID-19 deaths in 38 cities worldwide and found that in half of these cities, heat-related deaths could exceed annual COVID-19 deaths in less than ten years (at + 3.0 °C increase in global warming relative to preindustrial). In seven of these cities, heat mortality could exceed COVID-19 deaths in less than five years. Our results underscore the crucial need for climate action and for the integration of climate change into public health discourse and policy.