Laptop overheating in backpack

I have a 2020 MacBook pro purchased in July 2020. I turn off the WiFi, Turn off Dropbox Sync, shut down the laptop. I make sure it is shut down. I put it in my backpack. When I take it out two hours later the laptop is hot, and the battery power is significantly lower (say, 40% lower) when I take it out. This is a safety concern, especially during air travel, and it is a pain to lose the charge when I plan to work on the airplane. What is going on? How can this problem be addressed, so that SHUT DOWN actually shuts down the machine?