Certainly not a Harley jacket style but tend to wear a revit air jacket in northern va summers. Think their new summer model is now called the airwave. Quality build, decent stock armor, awesome airflow. Sizes run small as it's euro. Not cheap ($200 or so).
I got the Harley Rideready Mesh jacket for fathers Day it has pockets for elbow and shoulder armor and so far is very comfortable and cool in the heat. Nothing protects like Leather but I just can't wear a leather jacket on hot days.
I've got an Icon textile/mesh jacket with armour inserts along the spine and elbows/forearms. It definitely looks more like a sport bike jacket if you're standing next to me, but it's black on black so when you're riding I doubt anyone on the road could really tell the difference. Difinitely would provide the best combination of protection and light weight for hot weather conditions. For the most part I don't even really bother with it when it's really hot out, and will just roll with a t-shirt on. I'm sure if I ever dumped the bike like that I'd wish I'd been wearing it, but that's the way she goes.