Are your MacBook Pro's fans running at full speed when you experience overheating? You should hear quite a bit of fan noise. If not, it may indicate one of them has failed? There's only one fan if you have a 13 inch MacBook (I think?), 2 fans in 15 inch and above.
And when you say 'overheating' - is Premiere Pro crashing or just seemingly slowing down. Is your Mac crashing?
Keep in mind Intel MacBook Pros can run pretty hot and when they do they will throttle the processor quite significantly to handle the heat and also stop using Turbo Boost. Therefore - you will see a drop in performance when this happens.
If you have a case on the MacBook - take it off and see if there's any improvement. Ensure nothing your Mac is sitting on is blocking your fan ports.
An aging battery 'can' add to the thermal load on a laptop. Your battery should still be OK if it's had normal use - but something to consider. Test with it connected to power and see if any change.
Run Apple Diagnostics on your laptop - reboot holding 'D' key. Often this won't show any problems but worth doing anyway.
Consider upgrading your Mac to the latest version of Big Sur (Which I think is 11.6.8?)
One other thing - ensure you have the latest firmware for your particular model. I vaguely recall some thermal issues with some MacBooks of your era and there may have been a firmware update to resolve (or reduce) the issue.