|Source: NOAA Regional Climate Centers|
June 2015: 77.4666667ºF
June 2016: 77.45ºF
See, June 2016 wasn't really that bad!
I'm fairly certain that official monthly temperature records are based on temperatures rounded off to the nearest tenth of a degree, so June 2016 will be recognized with June 2015 as the hottest on record (at least until we beat it again in the future thanks to the warming climate). There are good reasons for rounding, including the fact that there is inherent uncertainty in the daily maximum and minimum temperatures arising from instrumentation error and calibration. For all intents and purposes, we really can't distinguish June 2016 from June 2015. That's OK. Misery loves company.