Today I rode my wife's Cross Check that has no rear rack. What's this mean? Backpack. What does backpack mean? Sweaty back.
I'm not sure how many of you are out there commuting with a backpack, but I strongly recommend buying yourself an inexpensive rack for your bike. I use a Planet Bike rack on all my bikes that cost about $25. I even have one for this Cross Check that I just haven't installed yet. Here's a tip, too. If you have multiple bikes you may want to use identical racks on all of them. I do that so that all my panniers are adjusted and work on every bike.
Even the cheapest rack will work to bungee on a plastic Walmart bag with your work clothes in it. And, in my opinion, that would be much better than a backpack.