Continuing the discussion that Brain's post and thread in the comments about the warmest minimum, the Brian neatly disposed of most of the contenders for 70ºF or higher. The one data point still standing was the University Experiment station on July 11, 1983.
Richard pointed out the min of 70ºF is at observations with both the minimum at Fairbanks International and College Observatory; at the time the College Observatory obs site was less than a mile and about 150' higher elevation.
However, an examination of the original observation form for the Experimental Station shows that the observation day low for July 11, 1983 should have been at least 65, as this was the temperature at the time of observation on the 10th (this should have been caught by NCDC at the time but was not).
The June 1991 heatwave produced several very warm nights. The highest calendar day minimum I can find is from the Cottonwood RAWS, located on a ridge north of the Yukon River (my memory is that it has been moved to its current location sometime after 1991 but I can't seem to find online documentation of that). On June 21, 1991 the lowest hourly temperature was 70ºF at 3am and 4am, However, RAWS platforms, then or now, do not record absolute temperature extremes: all we have to go on are the hourly observation. Offhand, I can't think of any why to query the RAWS archive (or SNOTELs) to get at the highest daily minimum temperature.
So, we're left with the low of 70ºF on June 25, 1992 at Fairbanks Airport as the only "continuously monitored" daily minimum temperature of 70ºF or higher. How does this compare with cooperative observations that day?
For June 25th minimum temperatures. we have
University Experimental Station 66ºF
Fairbanks Midtown 64ºF
Fairbanks Airport Upper Air: 58ºF
College Observatory: 58ºF
So this proves that the Fairbanks Airport data is bogus, right? Ahh, no. The hourly observations from the ASOS show 6-12 mph winds every hour from 10pm to 6am, which kept the air at the ASOS well mixed. The joy of mirco-meteorology.