A rough idle after high temperatures or an overheat could mean there is coolant entering the combustion chamber..
Considering how notorious 3.8L are for blowing head gaskets..
You might as well rule that out by testing the coolant for any sign of combustion gases..
Napa sells a Leak Detector Kit that you can use to test the coolant for any signs of combustion gases..
Click Here-->>Leak Detector Kit
It's pretty easy to use, even if you've never used one before..
There's a few video demonstrations of people using the combustion gas Leak Detector Kits on YouTube as well..
That's just one way to test for a blown head gasket..That's if
the gasket blew in that manner..
Check your oil level to make sure it does not rise..
If the head gasket blows in a manner where the coolant starts mixing with your oil, you can say goodbye to your bearings..
I hope it's not a blown head gasket, but you might as well try and rule that out..