Oh man, funny you should make this post, since I have had nothing but weird issues with my cooling system.
I feel your pain.
Best thing to do is literally empty all your coolant, and do a flush. Change your thermostat while you are at it just in case (only like 6 bucks) and just refill your coolant properly.
You have to make sure that you add coolant, run the car (with the pressure cap off [not the same as the regular cap to add coolant in])
and when it gets hot enough to open the thermostat, add some more. Drive it for about 5 mins, come back and add even more. It took me about a jug and a half of coolant to get it right.
It still acts slightly funny for the first 5 minutes I drive in the morning (and I even let my car warm up about 5 min before taking off). But it acts perfect after that...
I have a feeling it's just a common issue with the cooling system in these mustangs. If you get confused about properly re-adding coolant, just google it. I have seen some well explained guides.
Let me know how it goes or if you find something I didn't know about. I got mine running pretty well, but it bugs me that it isn't perfect.