In doing this research, I really expected 1936 to have the longest 90s stretch on record (1879-present). However, several embedded 85-89 days prevented 1936 from having the longest stretch.
Although 1936 is still the hottest summer on record and saw the hottest July on record AND it saw 13 consecutive days in the 100s (including 3 in a row of at least 110!), it did not have the longest 90 to 90s streak. That record belongs to 1983.
1983 was a hot & dry summer with many days in the 90s, including 4 days of 100-104. It was the hottest summer since the early 1950s before being surpassed in 1988 for heat & dryness.
Note the extent of above normal temperatures in 1983 when the heart of the heat occurred in mid to late summer:
Note how rainfall was below normal over a large area:
So here is the list of the top 10 longest stretches of consecutive days at or above 90 degrees.
Purdue University
1. 23 Days
July 9-31, 1983
2. 21 Days
July 10-August 2, 1901
3. 20 Days
August 7-26, 1936
4. 19 Days
July 18-August 5, 1940
5. 17 Days
June 16-July 2, 1933
6. 16 Days
July 25-August 9, 1931
July 14-29, 1934
July 3-18, 1936
7. 14 Days
July 18-31, 1919
June 23-July 6, 1934
8. 13 Days
July 6-18, 1887
July 13-25, 1932
June 28-July 9, 1949
August 10-21, 1995
July 21-August 2, 1999
9. 12 Days
July 25-August 5, 1887
September 16-27, 1891
September 5-16, 1897
June 30-July 11, 1911
June 20-July 1, 1941
10. 11 Days
July 3-13, 1881
June 16-26, 1910
June 24-July 4, 1931
August 1-11, 1938
July 25-August 4, 1941
July 11-20, 1980
June 27-July 7, 2012