In the Essence project a 17-member ensemble simulation of climate change in response to the SRES A1b scenario has been carried out using the ECHAM5/MPI-OM climate model. The relatively large size of the ensemble makes it possible to accurately investigate changes in extreme values of climate variables. Here we focus on the annual-maximum 2m-temperature and fit a Generalized Extreme Value (GEV) distribution to the simulated values and investigate the development of the parameters of this distribution. Over most land areas both the location and the scale parameter increase. Consequently the 100-year return values increase faster than the average temperatures. A comparison of simulated 100-year return values for the present climate with observations (station data and reanalysis) shows that the ECHAM5/MPI-OM model, as well as other models, overestimates extreme temperature values. After correcting for this bias, it still shows values in excess of 50°C in Australia, India, the Middle East, North Africa, the Sahel and equatorial and subtropical South America at the end of the century.