We examine the effect of the 20th and recent 21st century anthropogenic climate change on high temperature extremes as simulated by four global atmospheric general circulation models submitted to the Climate of the 20th Century Plus Detection and Attribution project. This coordinated experiment is based upon two large ensembles simulations for each participating model. The “world that was” simulations are externally forced as realistically as possible. The “world that might have been” is identical except that the influence of human forcing is removed but natural forcing agents and variations in ocean and sea ice are retained. We apply a stationary generalized extreme value analysis to the annual maxima of the three day average of the daily maximum surface air temperature, finding that long period return values have been increased by human activities between 1 and 3°C over most land areas. Corresponding changes in the probability of achieving long period non-industrial return values in the industrialized world are also presented. We find that most regions experience increases in the frequency and intensity of extremely hot three day periods, but anthropogenic sulfate aerosol forcing changes locally can decrease these measures of heat waves in some models.