Macbook Pro stuck in reboot loop, but can briefly boot up after sitting shut-down for several hours?

My 2013 Macbook Pro 15” is running Catalina, no recent updates or installations. Seemingly out of nowhere last night it entered a reboot loop, with the message “Your computer restarted because of a problem. Press a key or wait a few seconds to continue starting up.” After this I get a loading bar, which freezes around the 2/3rds mark, and the cycle continues. I tried SMC and PRAM resets to no avail.

After shutting down & letting it sit overnight I was able to boot successfully this morning with no special tricks, but within 5 minutes it was back to constant restarts. I achieved the same thing again after letting it sit for 2 hours. Both times, as the loading bar reaches the 2/3rds mark where it would normally restart, the screen dims & brightens twice.

Only things out of the ordinary that I can think of are that the battery’s getting old & the fan has been loud at times. I’m wondering if the fact that time spent shutdown helps (for a minute or two) could point to something like overheating rather than something corrupted? Thank you!