Older cars had a cable type system, when you choose heat you simply moved a knob/lever on your dash to the red side and you had heat, the reverse for cool air.
This knob was connected to either a vacuum line which ran down to a vacuum heater tap somewhere under the bonnet.
The lever was connected to a cable then to the heater tap.
When you move either you opened the heater tap or closed it.
Using this principle why wouldn't the IDOIT service people simply block off the heater line (you only need to block one off to stop the circuit) running off the engine and take the vehicle for a run with just the fan running and no A/C (you could even disconnected the wire on the A/C to stop it coming on altogether) and see if it blows hot air
if it does it's the engine soaking heat into the firewall of the vehicle and heating up that way.............your buggered in that case except to say that Jeep need to spend some money on some proper insulation...
if it doesn't blow hot air anymore it's going to be whatever turns the heat on from the engine (remember the old school heater tap above) maybe the the heater/AC air door actuators/gears broken faulty....or something that turns on and off as you select the temperature you require..
My 2015 SRT does the same thing, it's winter here in Aus I'll fix it in the summer..