A simple method is tested for scaling climate-extreme results from high resolution regional climate models (RCMs) to time-periods and emission scenarios for which the RCMs have not been run. The 30 yr mean relationships between indicators of extremes (IoEs) and annual mean daily maximum temperature (T-xa) are investigated. Such relationships from the UK Met Office Hadley Centre RCM HadRM3P, along with temperatures from the global climate model HadCM3, are used to scale IoEs to other time periods and scenarios. This is tested for selected indicators of heat-wave and drought over Europe for the period 1961-2099. Curvature is demonstrated in the relationships between these quantities and T-xa. Such non-linearities are shown to have a large potential effect on how these climate extremes are likely to evolve during the century, as well as their sensitivity to emissions. A broad picture of possible changes in European heat-wave and drought severity is presented. For drought over the Mediterranean and western Europe, a very clear positive curvature in the relationship between drought length and annually averaged temperature is found. (This feature is also common in a brief study of 6 other RCMs.) It suggests a rapid increase in drought length towards the end of the century, and a strong sensitivity to the emission scenario. Extended summer dry spells are projected to become a much more regular feature of western European climates. For European heatwaves, we find a slightly earlier onset of increases in heat-wave severity and a reduced sensitivity to emission scenarios than might be expected from a more straightforward interpretation of the Hadley Centre model results. This is linked with extreme dryness occurring at high summer in all years by the end of the century, but was not evident in the 6 other RCMs studied. Based on these results, suggestions are made for choices of future RCM experiments.