The surface temperature of the Greenland ice sheet is among the most important climate variables for assessing how climate change may impact human societies due to its association with sea level rise. However, the causes of multidecadal-to-centennial temperature changes in Greenland temperatures are not well understood, largely owing to short observational records. To examine these, we calculated the Greenland temperature anomalies (GTA[G-NH]) over the past 800 yr by subtracting the standardized northern hemispheric (NH) temperature from the standardized Greenland temperature. This decomposes the Greenland temperature variation into background climate (NH); polar amplification; and regional variability (GTA[G-NH]). The central Greenland polar amplification factor as expressed by the variance ratio Greenland/NH is 2.6 over the past 161 yr, and 3.3-4.2 over the past 800 yr. The GTA[G-NH] explains 31-35% of the variation of Greenland temperature in the multidecadal-to-centennial time scale over the past 800 yr. We found that the GTA[G-NH] has been influenced by solar-induced changes in atmospheric circulation patterns such as those produced by the North Atlantic Oscillation/Arctic Oscillation (NAO/AO). Climate modeling and proxy temperature records indicate that the anomaly is also likely linked to solar-paced changes in the Atlantic meridional overturning circulation (AMOC) and associated changes in northward oceanic heat transport.