We present an updated analysis of monthly means of daily mean, minimum and maximum surface air temperature (SAT) data from Greenland coastal weather stations and from a long-running site on the Greenland ice sheet, and analyse these data for evidence of climate change, especially focusing on the last 20 years but using the whole periods of available records (some since 1873). We demonstrate very strong recent warming along the west coast of Greenland, especially during winter (locally > 10 degrees C since 1991), and rather weaker warming on the east Greenland coast, which is influenced by different oceanographic/sea-ice and meteorological synoptic forcing conditions to the rest of Greenland. Coastal Greenland seasonal mean SAT trends were generally 2-6 degrees C, strongest in winter (5.7 degrees C) and least in summer and autumn (both 2.2 degrees C), during 1981-2011/12. Since 2001 Greenland mean coastal SAT increased significantly by 2.9 degrees C in winter and 0.8 degrees C in summer but decreased insignificantly by 1.1 degrees C in autumn and 0.2 degrees C in spring, during a period when there was little net change (<=+/- 0.1 degrees C) in northern hemisphere temperatures. SAT means for the latest 2001-11/12 decade were significantly in excess of those for peak decadal periods during the Early Twentieth Century Warm Period only in summer and winter, and not significantly greater in spring and autumn. Summer SAT increases in southern Greenland for the last 20 years were generally greater for maximum than minimum temperatures. By contrast, in winter, the recent warming was greater for minimum than maximum temperatures. The greatest SAT changes in all seasons are seen on Greenland's west coast. SAT changes on the ice sheet and a key marginal glacier closely followed nearby coastal temperatures over the last 20 years.