I have an idea of what could be wrong but that's going to be a lot of money!!! I was driving to work about a month ago when my fail safe kicked in and my check engine light came on. I looked at my heat gauge and it was pegged hot, I pulled it over it shut it down and after trying to get it home later that day after all seemed well we determined it was the thermostat. So, I changed the t-stat and took it for a little ride up the mountain and it ran fine and so it did the next day on a couple of drive on back roads. I thought all was well! The next two times I drove this truck in a two week period the initial heat up the truck it would go to the redline, I would pull the truck over in overflow coming out of the overflow tank and the top radiator hose would be ice cold. Then the t-stat would open up and I could feel the water rushing through the top radiator hose. The kicker is it would run fine over the rest of the day with no problems at all. I changed the t-stat one more time and the same problem are still there. The coolant level has been fine and looks fine. The engine oil looks good. I little bit of white smoke coming out of the exhaust. Can a blown head gasket cause the T-stat not to open up when it should?

It's a 03 F150 with 98,000 on it