Another option in conjunction w/backpack: a crate of some kind on the rear rack. I've got a milk crate that I used before I got my new backpack. The new bag doesn't fit. But I think I've found a solution to the sweaty back. An idea that I am whole heartedly recycling from one of the members here. Use one of those flat crates that vending machine companies use to haul their bottled beverages in.
There was one that was left behind at work. My backpack fit, so if that flat crate is still there when I clock out on Monday, I am going to *repurpose* that bit of plastic.