July 2020 MacBook Pro restarts in backpack after shutdown

I purchased a MacBook Pro in July 2020. If I turn off the wifi and shut it down, and wait until it is entirely shut down and only then close it up, it restarts after the lid is closed. If I put it in my backpack to travel, say on an airplane, it will go from 100% charge to 39% charge in 30 minutes of no use and become EXTREMELY hot to the touch. This is a hazard in flight. What is causing this problem? How can it be fixed? It appears to be (a) common, judging from other posts, and (b) incredibly unsafe.

If I just leave the machine closed on a table top, without touching it, I hear the startup tone after about 10 minutes. Then again after a while. Then again.

Does the machine need to be replaced under warranty, or is there another sure fix?