We had a piston APU in our DC-3, it provided electrical power for lighting, avionics and the air conditioners. We had window style air conditioners mounted in the foward and aft cabin bulkheads.
To be honest, I don't believe these air conditioners would be approved for aircraft use in this day and age. But thirty years ago you get away with a lot of things that are strictly forbidden today.
The majority of small jets do not have APUs, some have been retro fitted to have APUs installed and some newer versions of the older jets now have APUs as options. However, for the most part they are only for comfort during ground operations and are not required for normal aircraft operations.