Rear climate control fans blowing cold

warmth comes from the heater in the car
if it is climate control check the climate control module
check for heater control in the vent settings as the hot water tap may not be turning on

If you have owners manual check that your climate control settings are as you expect them to be, if that makes sense. Some on Fixya do not realise they gave climate control , they think they have normal A/C and try to correct chimerical problems. Please check and repost

Is your heater blower motor working on all speeds ? Are you get any air coming from the rear vents ?

There is a climate control module in the head liner of that vehicle. IT needs to be checked or replaced

Could be the controller or a faulty blend door.
The blend doors direct air thru the heater core and evaporator along with the vents. The controller uses electric motors to change the direction of air flow.

The resistor pack is to help control fan speed. Either your temp control door is stuck/unplugged which doesn't seem likely with rear blowing hot too. Could be temp sensor reading incorrectly, even then commanding full cold should do something. I would start with the person you just paid to work on it or you'll be paying someone to diagnose it.

Sounds like a bad blend door actuator. That's the motor that diverts air between the heater core and AC

Does the front blow cold ? Diagnosing rear problems
Taking to a qualified repair shop an having it diagnosed would be your best bet >

It may be getting low on freon sometimes they leak out

try changing the thermostat if thats not it check and see if you have water leaking in the passenger side floor board if so then you need a new heater core