Weather wise, it depends. Yosemite, Bishop, Joshua Tree, etc. are all too hot to climb in during the summer, or at least late summer. Is Chattanooga a different kind of heat? Dry versus humid?
It definitely gets hot in the mid-summer months, but not nearly as severely as other cities like Nashville, Memphis, Atlanta, even DC.
Also, I think calling Chattanooga "deep south" would be a severe misnomer.