Well, I'm far, Er,no wait..FAR from an authority, but it seems like you should be getting nearly the same temp on the cores output hose with the heat turned off. Maybe some of the cooling tubes are blocked.
I would see if theres anyway to get to the core without yanking the whole assembly, and see how it feels while running at temp. First step is removing the glovebox, but after that?? (I dont know how similar your year is, and havent tried taking mine arpart either, sorry)
Hope its of some help, and BTW, Welcome to the board.
J
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'66 Mustang Coupe- AKA "Lenore" *on disability for a (long) bit*
'93 GT Mostly stock AKA "Fawkes"
Rice Haters Club Member #239
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