I did a quick check of the Champaign-Urbana records and found no relationship between cool August weather and early frost. Since 1900 we have seen freezing temperatures four times in September (our average first fall frost is in mid-October). Of those four cases, August temperatures were below average in one case and above average in the other three. I experienced first-hand the September 22, 1995, early frost that ended the growing season in my garden. It was proceeded by an August with a monthly temperature of 78.9 degrees, 5.5 degrees above the 1981-2010 average!
However, in all four cases (1916, 1928, 1942, and 1995) the September temperatures were below average. So watch out for colder-than-average Septembers, not colder-than-average Augusts, as a possible sign of an increased risk of an early frost.
I will look into this in more detail in a future post.