Lakes impounded by natural ice dams occur in many glacier regions. Their sudden emptying along subglacial paths can unleash ∼1 km³ of floodwater, but predicting the peak discharge of these subglacial outburst floods (‘jökulhlaups’) is notoriously difficult. To study how environmental factors control jökulhlaup magnitude, we use thermo-mechanical modelling to interpret a 40-year flood record from Merzbacher Lake in the Tian Shan. We show that the mean air temperature during each flood modulates its peak discharge, by influencing both the rate of meltwater input to the lake as it drains, and the lake-water temperature. The flood devastation potential thus depends sensitively on weather, and this dependence explains how regional climatic warming drives the rising trend of peak discharges in our dataset. For other subaerial ice-dammed lakes worldwide, regional warming will also promote higher-impact jökulhlaups by raising the likelihood of warm weather during their occurrence, unless other factors reduce lake volumes at flood initiation to outweigh this effect.