The 3.0 Vulcan engine has had issues with fouling in the cooling system. I did a lot of research on it after my coolant went from green to brown in less than 6 motnhs and the heater core plugged. If you didn't crack the radiator or bust a hose, you may have shook some crap loose and plugged the thermostat. look at your coolant, is it green or brown? If it's brown, I would fluch the coolant system after removing the thermostat. Google Taurus Car Club, on their website is very specific directions on how to do it and it will back flush the heater core at the same time.
I had all maintenance records for mine, and when the heater core plugged, Ford refused to honor the warranty due to "neglect" even though there was a recall on them to install a bypass assembly (how this would prevent it I dont know) and to fluch teh coolant system with some chemical and refill. Now I just back flush the heater core and coolant system twice a year and let my son drive it as a beater while he is rebuilding the engine and tranny in his SRT-4.
gp