I never knew they designed stats to do that. Thanks!

 

A stuck blend door... the foam seal deteriorates and sticks the door to the box.
For me, it took quite a few times cycling the control hot, cold, hot, cold to break it free... then I got a pile of foam crumbs blowing out of the vents (still get the occasional chunk).

 

I have been dealing with this same issue.
+1 on anything Heyyou says. He helped with mine. I finally got the air out of my 96 5.2 and couldn't be happier.

Burp the system. It is VERY hard to do and time consuming. I bought a spill free funnel to help.

Get on a very steep hill and burp it. Since you have a new heater core, guess there's no need to flush it.