Did you change anything before driving it? Why not?
it's pretty simple to diagnose cooling system problems. take thermostat out, then run the car with the cap off for a while, make sure coolant is full and you can see it flowing through the radiator. After a couple of minutes any air in the system should be out, put the cap back on and see if you still have a problem. I'm willing to bet that will fix any problems.
If not... check to make sure that the fans are turning on when the car is at operating temp, considering it's cold outside i don't think this will be your problem. Because of the outside temp, you may have to let the car sit at idle to heat up enough to need the fans.
Do all of this BEFORE driving another 15 miles....letting your coolant reach 250* isn't something you want to do often.