It's definitely a busted heater core. Not an expensive replacement, but a pain in the ass job! First, remove the glove box door assembly. The heater core will be mounted to the inside firewall behind a cover that has screws.. And some of them are a pain to get to. Older ones are simpler. If it's too big a job, at least by then you'd have it started for the mechanic! Any roadside service shop can change it. No need for a dealer trip! Get the heter core and some new hose clamps and possibly heater hoses from autozone!
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