Also based on that page, the coolest July that Alabama has had was in July 1967, with an average of 76.1. The overall average for July is 80.0.
If you try to narrow it down to just Huntsville area, then the amount of data decreases to fewer years. However, you can see some historical data through the Alabama State Climatologis which puts 1966 as Madison County's hottest July at 84.0: http://nsstc.uah.edu/aosc/counties/madison.html
By contrast, the state-wide average for 1966 was 80.9, which is less than a degree above the standard. Weather is never simple.
How does June vs July vs August pan out when it turns out for hottest days? In recent years (see: http://nsstc.uah.edu/aosc/highest_st_temp.html) it has had a fair showing, but only fair.