One person says that fallout 76 was able to patch their game to fix a similar issue: https://www.reddit.com/r/xboxone/comments/d4yo4d/borderlands_3_overheating_console_on_xbox_one_x/f0hyh2q/

Ran Leviathan again today, this time with a supplemental cooling fan plugged into the back. [url=https://www.amazon.com/dp/B084GNJ36D]This is the fan on Amazon[/url] My xbox overheated in the void realm / shadow realm again. First time, I went into shadow realm, and lasted long enough to do my callout from the symbol on his forehead. Then powered off. Then after rebooting, I changed assignments to stay in the throne room. At one point we were wiping, I died, but one guy was still in the shadow realm. I changed my camera over to watch him in there and my xbox overheated and powered off again. Same thing also happened to a teammate, but not only did he power off in the void realm, he also overheated and powered off while doing the final run at gauntlet. I guess I can try cracking the case open and seeing if there's any dust inside? Or, has anyone used a supplemental cooling fan that actually worked?

We ran Leviathan again on Sunday. This time, when all 6 of us went into the final gauntlet run together, both my xbox and another teammates xbox shut off due to overheating. I bought a supplemental cooling fan for the xbox one off of Amazon, but I didn't have it plugged in or turned on at the gauntlet encounter, so I don't know if it would have worked or not. I'm hoping to try it next weekend.

also try vacuuming the vents of your console of the dust.

temporary workaround is to teleport out right away.

Had the same happend to me yesterday, run 3x times just right after the 1st callout the xbox turns off, one of the instance a fireteam member, also with an X, had the same problem, booted exactly at the same time, with the same overheating message.