The car overheated, the water didn't seem to be flowing and was backing out of the overflow, etc., so I checked the thermostat. It came out in 2 pieces, without the copper actuator (which I never found). I replaced the thermostat with a new one and it overheated again. I took the radiator out and it seemed to have good flow and the actuator wasn't in there. I checked the new thermostat by boiling it in water and it didn't open. I bought a 2nd new thermostat and checked in boiling water and it opened (I also checked the 1st new one again at the same time and it still did not open). I ran the car with no thermostat for 45 min. and it didn't overheat, but idles very rough. We took it for a test drive, it drives well at higher speeds but still idles very rough. Could this be a sign of damage from overheating (valves, lifters, etc.) or could some fuel sensor been affected making it run rich?  

Well anything is possible further,,,, but it sounds as though its unrelated. I am not that familiar with your engine but the first thing I would check is IAC(Idle air controller). These generally control your idle and they arent that expensive. Make sure you dont have any vacuum leaks(check all hoses-shut them off for test-like brake vacuum booster may be leaking) and then do a fuel pump pressure test.  

Those three things cover some ground I know Further,,,,but they will get you started and they probably cause about 75% of the idle problems.  

Well that gives some ideas, thanks.

It sounds like overheating isn't likely to cause the problem, which was what I was worried about.

Thanks!  

Idling problems can be caused by a number of things.  What year is that engine?  A carbureted engine will have different symptoms and fixes than an EFI engine.  

He said it was a 91 Soaring and 1985 was the last year for carbureted mustangs.  

Oh, Ok.  Then the first thing to check would be the IAC.  If that is good, then take it to a Ford house and have them hook it up to their 'puter.  

I'll check or replace the IAC, then go from there.

Thanks to all for the help.