Heat and air

Hi and thanks for using two 2CarPros.com. Based on your description, there is a good chance the blower motor resister is bad. On these vehicles, power is directed to the blower motor and then using different ground paths, the power goes through the resister at different points causing the fan to speed up or slow down. I have had situations very similar to yours where the resister melted down internally creating a constant path to ground. Therefore, the fan would not turn off.

Here are the directions for removal and replacement specific to your vehicle. There are two pictures attached which correlate to these directions.

CONVERSION CALCULATOR

2005 Jeep Truck Grand Cherokee 4WD V8-4.7L VIN N
Vehicle » Heating and Air Conditioning » Blower Motor Resistor » Service and Repair
Service and repair
Removal
Warning:
On vehicles equipped with airbags, disable the airbag system before attempting any steering wheel, steering column, or instrument panel component diagnosis or service. Disconnect and isolate the negative battery (ground) cable, then wait two minutes for the airbag system capacitor to discharge before performing further diagnosis or service. This is the only sure way to disable the airbag system. Failure to take the proper precautions could result in accidental airbag deployment and possible personal injury or death.
The blower motor resistor may get very hot during normal operation. If the blower motor was turned on prior to servicing the blower motor resistor, wait five minutes to allow the blower motor resistors to cool before performing diagnosis or service. Failure to take this precaution can result in possible personal injury.

CAUTION: Do not operate the blower motor with the blower motor resistor removed from the circuit. Failure to take this precaution can result in vehicle damage.

Disconnect and isolate the negative battery cable.
Remove the glove box from the instrument panel.
Disengage the wire harness connector locking tab (1) and disconnect the wire harness connector (2) from the blower motor resistor (3).
Remove the two screws (4) that secure the blower motor resistor to the HVAC housing (5).
Remove the blower motor resistor from the HVAC housing.
INSTALLATION
Position the blower motor resistor (3) into the HVAC housing (5).
Install the two screws (4) that secure the blower motor resistor to the HVAC housing. Tighten the screws to 2 N.m (17 in. lbs.) .
Connect the wire harness connector (2) to the blower motor resistor and engage the wire harness connector locking tab (1).
Install the glove box into the instrument panel.
Reconnect the negative battery cable.

I hope this helps. Let me know how you make out with it.

Take care,
Joe