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Very possible for a head gasket problem, go ahead and do a cylinder leakdown test to confirm it, and you may discover it before your testing is done when you pull plugs out and steam is present or plugs show signs of water / ethylene glycol.
Thanks for your question,
I haven't seen one with that associated problem, unless the fins on the pump are deteriorated and not pushing the coolant fast enough.
2003 Jetta left rear window blue plastic part of the