When you add an additional display, the additional DATA required can be enormous. But screen refresh is handled by a rasterizer/display-generator automaton, and the processor only intervenes once a screenful. This does not add a measurable computing load to your Mac.
On the 2019 model 16-in MacBook Pro,. it may switch the display Memory into high gear, and generate additional heat.
Your issue is more likely to be caused by other problems. Rather than play 20 questions, consider downloading and running this little "discovery' Utility, Etrecheck. It fixes NOTHING. Its only reason for existence is to create report that can be scoured looking for clues to problems.
IF you can follow its directions precisely, it will generate a SANITIZED report (free so all personally-identifiable information) that can be posted back to the forums for Readers to analyze.
How to Use Etrecheck Pro for free