First of all when you manually control the unit can you get all of your fan speeds? Ie does it ramp up and down properly?
And what heat are you using? If you use the defroster you will always use the A/C because it removes the moisture from the air first then heats it up. Not sure if it uses that with the other modes with the auto hvac system. My truck has the manual system and only uses the A/C system when using defrost. When using the floor or vents the A/C is not used. In my CTS it uses the A/C in all settings I do believe with its auto HVAC system.
I would start with the heater core... Having warm/hot lines mean absolutely nothing. Since the coolant is in contact with the coolant in the pipes going to the heater core they will always be warm. Best way that "I" know of to test for plugged heater core is to disconnect the lines from the heater core at the firewall and try pouring distilled water through each line. Best way to do that is to get a piece of hose and a funnel and just pour it in. Be aware if you use tap water as coolant or to flush with that it contains many chemicals such as chlorine, fluoride, phosphates. Depends on your water source. Ground water tends to be heavier in things like Lime and Iron. Most water systems coat old pipes by including Phosphates in the water (Except Flint, MI....) So understand that tap water is very bad to use because the corrosive components such as chlorine and the coating components such as phosphates, limestone, iron and just about anything else.
I suspect you have a plugged heater core due to using tap water or you have the original dexcool still. Especially if the dealer says the system works fine when they tested it.
While you COULD have a short, unless you have had a serious accident with that vehicle, have pulled the dash apart, or have flooded with water it is not likely.
So test that the heater core is actually flowing coolant. Also check that your coolant level is full. If your coolant level is too low the heater core will not get any heat through it either... And loss of coolant can be something simple to fix like a water pump or a dreaded cracked head if your "lucky" enough to have the 706 casting heads. (Look at front of passenger side head for the number.) My truck has this casting and with 263k miles has not cracked as I had originally feared a month ago. I just had a bad water pump.
Anyhow, first check coolant level, flow test your heater core and come back with results...
Oh and
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