The influence of anthropogenic climate change on both mean and extremely hot temperatures in Europe has been demonstrated in a number of studies. There is a growing consensus that high temperature extremes have increased more rapidly than the regional mean in central Europe, while the difference between extreme and mean trends is not significant in other European regions. However, it is less clear how to quantify the changes in different processes leading to heat extremes. Extremely hot temperatures are associated to a large extent with specific types of atmospheric circulation. Here we investigate how the temperature associated with atmospheric patterns leading to extremely hot days in the present could evolve in the future. We propose a methodology to calculate conditional trends tailored to the circulation patterns of specific days by computing the evolution of the temperature for days with a similar circulation to the day of interest. We also introduce the concept of residual trends, which compare the conditional trends to regional mean temperature trends. We compute these trends for two case studies of the hottest days recorded in two different European regions (corresponding to the heatwaves of summer 2003 and 2010). We use the NCEP reanalysis dataset, an ensemble of CMIP5 models, and a large ensemble of a single coupled model (CESM), in order to account for different sources of uncertainty. We also evaluate how bias correction of climate simulations influences the results.