We have used extensive air temperature measurements (~  1400 station-years) to assess more than 10 gridded datasets over the Greenland ice sheet. We recommend the best datasets for estimating past melting of the ice sheet and show that choice of dataset is important for evaluating 31 earth system models. Most, but not all, of the datasets show similar history of temperature changes over the 20th century, and the earth system models generally capture long-term warming but not decadal variations.