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Anthropogenic climate change is a key threat to global biodiversity. To inform strategic actions aimed at conserving biodiversity as climate changes, conservation planners need early warning of the risks faced by different species. The IUCN Red List criteria for threatened species are widely acknowledged as useful risk assessment tools for informing conservation under constraints imposed by limited data. However, doubts have been expressed about the ability of the criteria to detect risks imposed by potentially slow‐acting threats such as climate change, particularly because criteria addressing rates of population decline are assessed over time scales as short as 10 years. We used spatially explicit stochastic population models and dynamic species distribution models projected to future climates to determine how long before extinction a species would become eligible for listing as threatened based on the IUCN …