What should be done when clothes wrinkle from being too long in a tumble dryer?
Steam is the best agent for getting wrinkles out of clothes, but dry heat comes in a distant second.  Many newer dryers have a dedicated "touch-up" setting, which runs at medium-to-high heat for about ten minutes, precisely because it's very common to leave clothes in the dryer overnight.  That touch-up will be a dry heat, of course, so it's not quite as effective as steam, but you'll be amazed at the difference it makes.

Adding a wet (wrung out or from the spin cycle - NOT sopping wet!) towel will improve your results significantly, but you'll need to 1) run the dryer for a bit longer to allow the wet towel to start steaming, and 2) steer a careful course between letting your other clothes get wet, and letting the whole batch get dry.  

I would pop in the towel and start the dryer, then come back in 10-15 minutes and start pulling clothes out a few at a time - letting the dryer run in between while I folded or hung them up.  Leave the towel for last; if you have another load waiting to dry, let it finish with that load.