From NOAA’s Global Climate Report – June 2020:
Averaged as a whole, the global land and ocean surface temperature for June 2020 was 0.92°C (1.66°F) above the 20th century average of 15.5°C (59.9°F), tying with 2015 as the third highest June temperature departure from average in the 141-year record.
Nine of the 10 warmest Junes have occurred since 2010; the seven warmest Junes have occurred in the last seven years (2014–2020).
The June 2020 global land-only surface temperature was also the third highest for June at 1.29°C (2.32°F) above average. The global ocean-only surface temperature of 0.77°C (1.39°F) was also the third highest for June in the 141-year record.
The links in the quotes are to the related time series data.