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Previous attribution studies of heat-related excess mortality have given limited attention to temporal trends in vulnerability and their non-climatic drivers. Here, we address this gap by combining counterfactual temperature data derived from multidecadal reanalysis series with time-varying warm-season temperature-mortality associations for the 15 most populous cities in Germany over 1993-2022. We find that declining vulnerability, associated with improvements in life expectancy, has led to decreasing trends in heat-related excess mortality in most cities despite summer warming. In contrast, if life expectancies had not improved, climate change would have induced increasing trends in the heat-related death burden. The growing anthropogenic fingerprint also emerges in the relative proportion of heat-related excess mortality attributable to climate change, which increased by 5.6% per decade (95% confidence interval: 2.6%, 8.6%), averaging 53.6 % (49.8%, 58.9%) across the study period. Our results underline the importance of accounting for evolving vulnerability when attributing human health outcomes to climate change.