We have 50 dates for the hottest day all time in each of the 50 states. Here is a breakdown of that data by number of days in each month when heat records have been broken.
Hottest Months of the Year in the United States
July - 31
August - 10
June - 7
September - 1
April - 1
First the April date is for Hawaii so it's not really relevant. The record the hottest temperature ever recorded in Hawaii was 100 degrees in Pahala on April 27, 1931.
By far, July leads the list with 31 record setting hottest days. August is second with 10 and June is third with 7. Looking more closely at the data all of the June dates occur from the 27th to the 30th of the month. So really in June we are only talking about the last 4 days of the month.
Similarly, in August all the dates occur on or before the 12th of the month except for one on August 21, 1983 when it was 112 degrees in Fayetteville, North Carolina. Including that date, the 10 dates in August when an all time record temperature was recorded in a state averages out to just 8.9.
On September the 5th in 1925 it was 112 degrees in Centerville, Alabama. That is the only record setting hottest temperature date in September, and while most of September does fall in Summer it appears that date is rather fluky since it is the only date in September and it's over 2 weeks past the last date recorded in August.
The 31 record setting hottest dates in July are spread out all over the month with the average for all 31 dates being 14.68. Just about right in the middle. The whole month of July is hot and a record setting temperature can happen at any time in July.
The hottest month of the year in the United States is clearly July. Something most people already know and the data clearly confirms it.
What the data also shows is that the hottest time of the year in the US stretches for just about 7 weeks running from the last four days in June through the 12th of August. If a record setting hottest temperature of all time is going to be set in any state outside of Hawaii this year it is highly probable it will occur over that 7 week summer stretch.
As the dates for North Carolina and Alabama show, a record setting hottest date can occur outside of that time frame but out of 49 dates those are the only two. Two out of 49 is only 4.1% so the odds are very high that a record setting hottest temperature for any state will occur between June 27th and August 12th in the United States if it is going to occur at all.
And though the odds are not quite as high it also probable that any new record setting highest temperature will also occur during July the hottest month of the year in the United States.
Sources: http://www.usatoday.com/weather/wheat7.htm
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