2002 A6 2.7T. We had a cold snap it got down to negative 18F on the way home last night. About half way home the temperature started to climb. So I turned the heat to max and set the air to all vents (defrost, dash and floor).
Once I got closer to town I took a side road home and the temperature went back to normal.
The next morning I started the car let it warm up (It was negative 20F).
Started the drive to work and by the time I got on the highway I did not have any heat and it was starting to overheat so I got off at the next exit and let the car cool off then headed back to town. The car did got hot enough to pop the radiator/reservoir cap and leak coolant
Any ideas what would cause this?

I am thinking the T-stat.
Thanks for the help