Look into mesh jackets.
I wear a
Firstgear Tex 3 jacket that I bought at the local Cycle Gear store here in Tulsa. They had it on sale for just over $80. I think they discontinued that particular jacket now, but Firstgear replaced it with the
Control Mesh. They have a good selection of minimally-priced armored jackets that are pretty sturdy. I ride nearly every day here in midday heat and very seldom have any sweat issues other than on my head (from the FF helmet). It also comes with a zip-out liner that rolls up tiny and makes it warmer if you find the need.
The problem a lot of people have with mesh jackets is a real lack of abrasion resistance. Honestly, a good vented leather or textile jacket will be better for this, but when you're faced with either suffocating or not wearing your jacket, most people will go with the latter, and at least some armor protection is better than none at all. I have no problem wearing a mesh jacket, and combined with a pair of meshed or perforated gloves, it keeps me pretty cool, even in midday traffic.
Check out the jackets at NewEnough.com or Cyclegear.com and then go try some on at a store or a dealership. Fit is everything, and most of the street jackets are alpha-sized. You really have to try them on and get them just right. I hear NewEnough has a great return policy on stuff if it doesn't fit though. I'll probably buy online near the end of the summer when I'm looking for an autumn and winter jacket.
There are a lot of good gear stores online if you're comfortable buying fitted clothes without trying them on.
NewEnough.com
Cyclegear.com
motorcycle-superstore.com
DennisKirk.com
MotorcycleGiant.com
BikeBandit.com