Hey there, sports_Researcher!
Thanks for reaching out in Apple Support Communities! We understand your MacBook Pro is overheating when connected to an external display. We'll do our best to help out with this!
Have you had a chance to test if this persists when using a different cable to connect the two devices? Does the behavior continue?
Also, we recommend using the following support article to further assist when your MacBook is overheating:
Keep your Mac notebook within acceptable operating temperatures - Apple Support
If this persists, you can connect to another display to further isolate the issue and determine if the issue is with the Mac or the display.
Still need help, Contact Apple Support for next steps.
Kind regards.