The summertime thaw depth of permanently frozen ground (active layer thickness, ALT) is of critical importance for natural hazard management (e.g., rock avalanches) and construction (foundation stability) in mountain permafrost regions. We report the first analytical heat transport model for simulating ALT based on near-surface temperature in permafrost rock walls. Our results show that the ALT will likely increase by more than 50 % by 2050 at 3000 m a.s.l. in the European Alps.