Re: Umm... nope.
Sure, that xkcd graph was certainly smoothed, which is reasonable when presenting trends over 1000:s of years.
VERY well-known post-WWII drama of 30yrs sharp global cooling ...
Where can one see that? A graph from NASA (https://climate.nasa.gov/vital-signs/global-temperature/) shows a little upward peak around WW2, after which the steady upward trend that existed before the war seems to resume.
About the times of William the Conqueror, we already are above the circa-1000 temperatures according to several graphs. Greenland is not yet green again, but it probably is in a few decades. We shall see about the snow in Norfolk. It may get rarer, but on the other hand snowfall is also affected by weather patterns, which may change so that despite the warming, you still get snow in winter. In Helsinki where I live, there actually tends to be more snow if the Gulf of Finland has remained longer uncovered by ice due to a warm autumn. More moisture gets picked up from the open sea compared to an ice-covered one, and falls on the land as snow.