Spandex. No they don't. If the APU isn't working and it gets hot, so do we. If you are in a small cabin jet or turboprop you won't have an APU anyway - high summer and mid winter you will cook/freeze and be writing the tech log at night with a torch in your mouth. Oh, the glamour....
Most business jets start on electric power, not bleed air so a GPU or battery will do the job of getting the engines going if necessary.