Extreme weather events are triggered by atmospheric circulation patterns and shaped by slower components, including soil moisture and sea-surface temperature, and by the background climate. This separation of factors is exploited by the storyline approach where an atmosphere model is nudged toward the observed dynamics using different climate boundary conditions to explore their influence. The storyline approach disregards rather uncertain climatic changes in the frequency and intensity of dynamical conditions, but focuses on the thermodynamic influence of climate on extreme events. Here we demonstrate an advanced storyline approach that employs a coupled climate model (AWI-CM-1-1-MR) where the large-scale free-troposphere dynamics are nudged toward ERA5 data. Five-member ensembles are run for present-day (2017–2019), pre-industrial, +2K, and +4K climates branching off from CMIP6 historical and scenario simulations of the same model. In contrast to previous studies, which employed atmosphere-only models, feedbacks between extreme events and the ocean and sea-ice state, and the dependence of such feedbacks on the climate, are consistently simulated. Our setup is capable of reproducing observed anomalies of relevant unconstrained parameters, including near-surface temperature, cloud cover, soil moisture, sea-surface temperature, and sea-ice concentration. Focusing on the July 2019 European heatwave, we find that the strongest warming amplification expands from southern to central Europe over the course of the 21st century. The warming reaches up to 10 K in the 4K warmer climate, suggesting that an analogous event would entail peak temperatures around 50 ºC in central Europe.