It's not that they like to use rebuilt heater cores. It's the fact that they are cheaper.
Tell them to put some die in the coolant and then they, or you if you want to get a blacklight and look under the dash yourself, will know exactly where it's coming from. The problem with most shops and even dealerships is in the fact that they see a problem with something, find the fix, then assume every vehicle that comes in with that particular symptom is the same problem.
FYI..
The Lemon Law "Period" is 24months after the original date of DELIVERY as a new vehicle.
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"Genuine" ASE certified Mazda, Hyundai, Isuzu Technician
Escort Enthusiast Site
Automotive Electrical Specialist, Tuning Specialist