Sorry, but it's likely the heater core. On '64's, the cores fail often if there is no restrictor added to the smaller hose t slow the flow into the core. I've replaced many until I figured out how to fix the problem.
Take a piece of round stock, plastic or metal, 5/8" diameter, about 1" long. Drill a hole through the center about 3/16" to 1/4" in diameter. Put that restrictor inside the small hose at either end. You'll not have the core fail again.
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BONESTOCK GOATS
'64 GTO Tripower Hardtop (Wife's Car)
'64 GTO Tripower Post Coupe (My Car)
'99 Bonneville SE Sedan
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