Overheating and Rough Idle!?

It might. An engine running hot can run erratically.

First check your coolant level, then change your T-stat. And if you haven’t flushed your coolant out with fresh coolant for a few years, you might want to do that when you change your T-stat.

Also, when was the last good tuneup? Are the sparkplug wires original? Rotor? Distributor cap?