I've had that happen in two different vehicles. In each case, the head gasket was leaking into the coolant passages, not the oil chambers in the head/block. I was getting bubbling into the overflow tank and coolant was being forced out. In one case, one garage tried to tell me that the rad was plugged and didn't pay any attention to my story about the bubbling into the tank. My dealer used an air pressure test to diagnose the real problem. New head gasket, problem solved, but no water in the oil.
I don't remember if it overheated, but I don't think it was significant. We had to drive back home with it acting that way and that was a 2-day trip. As long as I stopped on occasion and filled everything up with water, it was fine (sort of!).
Dave