Global temperatures aren’t strictly seasonal because they are a monthly anomaly for the whole globe, so I reckon any seasonality should be cancelled out of them and there would be little point in looking for the warmest calendar year, so I prefer to look for the warmest twelve month period by means of a moving average. As you can see from these screenshots from my Global temperature application, the warmest twelve month period actually occurred between September 2015 and August 2016 in the HadCRUT4 series with an average of +0.882°C. Try as it might 2020 couldn’t get even close to 2016, and the highest it reached was +0.807°C between June 2019 and May 2020, which fell 0.075°C short of the 2016 figure, in global temperatures terms that minute fraction was as wide as a country mile. The GISTemp4 series got slightly closer to 2016. During the summer the 12 month average anomaly reached +1.053°C for two consecutive months and very close to the +1.073°C that occurred between October 2015 and September 2016. So 2016 prevailed again.
The ERA5 data series from Copernicus came closest of them all in finding 2020 warmer than 2016, but even in this series the +0.656°C during the warmest twelve months from October 2015 to September 2016 still prevailed over the recent warmth from June 2019 to May 2020 by just one thousandth of a degree!
So in conclusion the warmest 12 month period globally occurred between September 2015 and August 2016.