Mean-state warming loads Germany’s extreme-summer heat burden

European summers are warming rapidly, increasing the frequency and intensity of hazardous heat. Here we quantify how mean-state warming has increased Germany's summer extreme-heat burden and how that risk scales with global warming level (GWL). We introduce OMS (Observation-based Mean-Shift), an observation-based counterfactual framework that preserves observed day-to-day weather variability while shifting only the seasonal mean state. Using OMS, we quantify Germany's sensitivity of June--August mean temperature to global mean surface temperature and translate observed summers to pre-industrial, +1.5 °C, and +2.0 °C climates by shifting the observed daily JJA series. Because only the seasonal mean is adjusted, OMS isolates the thermodynamic signal while leaving circulation statistics unchanged, providing a conservative baseline.
Germany exhibits strong regional amplification, with an estimated sensitivity of +2.63 °C of local summer warming per +1 °C of global warming and a 95% confidence interval of 1.62–3.62. To connect warming to exposure-relevant outcomes, we define the extreme-heat burden, EHD, in °C·days as cumulative degrees above a fixed national summer 95th-percentile threshold for 1991–2020. We evaluate the high-impact summers of 2018, 2019, and 2022, producing warming-level-consistent counterfactual realizations for each event while retaining intra-seasonal variability. Across these events, anthropogenic warming yields a substantial increase in EHD from pre-industrial to present-day conditions, with sharp further escalation toward +1.5 °C and +2.0 °C. Subnational analyses show coherent increases across all federal states but with substantial heterogeneity in magnitude, highlighting where risk intensifies most strongly as warming progresses. We additionally quantify per-capita burden using population data and assess distributional equity using Lorenz curves and Gini coefficients. Gini coefficients show that total extreme-heat burden is distributed fairly evenly across years, whereas per-capita extreme-heat burden is notably more concentrated. This implies that while the overall hazard is broadly spread across federal states, population-normalized exposure is substantially more unequal, with a disproportionate share of per-capita heat burden concentrated in a subset of states.