Keeping anything on your back will make you sweat. Plus, messenger bags aren't meant to be carried where the models at the Timbuk2 link are carrying them. They carry better higher on the back, more like a backpack.
A better solution might be to put a rack on your bike and bungie the backpack to that or zip tie a milk crate to the rack and put your current backpack in there. for a cost effective solution, can't beat the milk crate!
Now if cost isn't an issue, check out the briefcase panniers by Axiom, Arkel and Ortleib. There have been a couple threads about them recently. I'm openly an Arkel fanboy and if I had to do it again, I'd save the money on the Timbuk2 Commuter bag I got from REI last fall and purchase the Arkel Briefcase.