Originally Posted by
unterhausen
I was also going to suggest heating the cup only. The crud in the threads loosens up when you do that, it's not just the thermal expansion. I have done this on a car with great success. Don't kill the paint if you don't have to.
+1
A few other tips if you haven't got it out yet is to use a dead blow hammer and to hold whatever tool you use tight to the cup with some sort of bolt.