I have one of those backpacks with an internal frame and mesh back panel that lifts the pack off of my back to allow for free airflow between the two. My back still gets sweaty when I ride (I'm a sweaty guy in general), but the free air gap does help in that regard.

Most of the guys on the tour thought I was nuts for doing it with a backpack, but it really is the way that I'm happiest on a bike. I like the performance of a lightweight bike too much. When I first started commuting, I used a rack and trunk bag, but once I went to a backpack, I never went back.

It helps to invest in a really nice backpack.