Global and regional climate models are deterministic physical models which provide predictions of, amongst other things, future temperatures under a range of climate change scenarios. Predictions are available on grids with cells ranging from XX to YY (GCM) and XX to YY (RCM). The way in which these models are fitted means that they are often good at predicting changes in the mean temperature, but less good at predicting the behaviour of unusual events. Accurate predictions of such events is of particular importance in polar regions, as they can lead to increased ice melt which, in turn, leads to sea level rises. In a recent comparison of observation data and regional climate model output in Greenland, it was observed that regional climate models underestimate the sizes of extreme temperature events, and hence will underestimate future return levels. To resolve this, we fit a statistical downscaling model, based on existing extreme value models, which shows quite marked success in improving estimates of return levels, when compared to the naive approach of using the RCM output directly. Results focus on a single location in Greenland (Summit), but consider four sets of RCM output.