Greenland's temperature history has been discussed recently at WUWT. It is another region which is sparsely covered by measurements in GHCN, but has better numbers in the recent NCDC GSOD data which Ron Broberg has made available.
At WUWT Steve Goddard was criticising NASA for observing that temperatures had risen rapidly in the last 30 years. He didn't actually say whether this was right or wrong - he just said that nett movement since 1920 had been negative. So with GSOD data for the more recent coverage, let's see.
Here is the picture that NASA showed. They were commenting more on the rise in the seas around Greenland than the island itself for which the rate of rise shown is rather lower.:
Caption:Few places on Earth are warming faster than the Arctic. Temperatures have been rising several degrees Celsius per decade (red areas) since 1981. Among the most fundamental questions about Arctic climate change is how the warming will affect the Greenland Ice Sheet. (NASA Map by Robert Simmon, based on data from Josefino Comiso, GSFC.)
Here is the GHCN record for Greenland from 1901. It's true that it shows a marked warm period in the 1920's, and probably if you start a trend there to present, it would be negative.
On the other hand, coverage is poor - mostly 5 stations up to about 1940. And we're about back to that now.
Looking at the time period NASA was actually talking about, from 1981, then yes, there is a period of rapid rise from about 1990 to 2005, with some decline since, and ups and downs in the 80's.
Although GSOD has more stations, they are mostly W coast. GHCN seems to have a better distribution. In fact, GSOD counts as Greenland Jan Mayen and an island near Svalbard; I took them out for consistency.
It's likely that NASA's plot uses satellite data, which is probably necessary since stations are restricted to the coast.
Certainly it's hard to see a rise of several degrees per decade on land from the instrumental record over thirty years, although the peak rate would reach that. But in fact NASA's color scheme seems to show about 1C/decade on land.