The analysis of extremes in climate models is hindered by the lack of statistics due to the computational costs required to run simulations long enough to sample rare events. We demonstrate how rare event algorithms can improve the statistics of extreme events in state-of-the-art climate models. We study extreme warm summers and heatwaves over France and Scandinavia with CESM1.2.2 in present-day climate. The algorithm concentrates the simulations on events of importance, and shifts the probability distributions of regional temperatures such that warm summers become common. We estimate return times of extremes orders of magnitude larger than what feasible with direct sampling, and we compute statistically significant composite maps of dynamical quantities conditional on the occurence of the extremes. We show that extreme warm summers are associated to wavenumber 3 hemispheric teleconnection patterns, and that the most extreme summers are related to the succession of rare subseasonal heatwaves.