All current/former residents of the South: can the heat make you sick even with a/c?

I grew up in Raleigh, and as a child I used to get sick from the heat, but we didn't have a/c. Now I'm fifty, and considering moving back. I just came from visiting Georgia, and although I would be inside 95% of the time, with good a/c, I did feel a little unwell during the visit and so I'm curious. If you're inside almost all the time, with a/c, does that mean it's basically the same as if you are in a cool climate, or does the heat and humidity still affect you?