I have seen a cap cause this, even in colder weather in a different Ford, an Aerostar. I had the head gaskets replaced only to see the overflow tank overflow again. My dad, a lifelong mechanic said, "replace the radiator cap with an OEM spec cap and your problem will go away". Dad was right. I spent a lot on that one, I should have asked dad first!
I had a similar problem with my XR2 two winters ago. It blew one of the small coolant hoses for the turbo, and I thought everything would be fine after I replaced all the small coolant hoses. It was about 30 degrees below freezing (0 deg Fahrenheit) for the whole week following, and I was having coolant overflow every day that week when I got home from work (25 miles). At first I thought the system just had some air trapped within it, but eventually I figured out that the coolant temperature sensor (the one that informs the ECM) had failed, and that was what caused the blown hose in the first place. Once I replaced the sensor (RockAuto was less than $20) the problems ceased.
Check the specified resistance of that sensor.