I have a 2007 Lincoln MKz. I had thought the waterpump went out and had no choice but to drive it home.
Well,it overheated of course but then it did something strange and the temp gauge went back to the middle and the heater started blowing hot air again . After about 2-3 minutes it went out again and started blowing cold air and overheated again.
Could this be electrical or possibly heater core related.
I may be reaching out I don't want to have to change the waterpump
Had a few with your symptoms after overheating and it was the head gaskets . Took a fair bit of diagnosing before I found the cause , a small leak / blow on the gasket gradually pressurising the system When driving it caused an airlock which affected the cooling system and heater , then as pressure released temporary when stopped or whatever , heater would function again . Might not be your fault , but a block test will confirm or not