My estimate for June's GISTEMP, using the daily University of Maine Climate Reanalyzer data, is 0.83°C.
That would be a record for the month, above June 1998's 0.75°C. The 1998 El Nino isn't looking so remarkable anymore.
This estimate, if accurate, would also be the 6th-warmest of any month in GISS's records, which start in 1880.
We'll see. I wasn't very close last month -- too high by 0.12°C. Here's my record so far; my overall average is very close, but for individual months not as much: