My engine fan would be running after I shut the car off

I would also check the cooling fan motor to see if it is working. Check out the diagrams (Below). Please let us know what happens.

https://www.2carpros.com/articles/replace-electric-fan-motor

It should come on at 208 degrees and off at 190.

I attached a wiring diagram of the system for you to view.

https://www.2carpros.com/articles/how-to-check-a-car-fuse

https://www.2carpros.com/articles/how-to-check-an-electrical-relay-and-wiring-control-circuit

Engine Coolant Fan Motor Replacement

This vehicle is equipped with counter-rotating engine cooling fans. The right hand fan will require the use of GE-47827 for fan blade removal. The left hand fan blade can be removed using a normal six point socket.

Removal Procedure

Caution: An electric fan under the hood can start up even when the engine is not running and can injure you. Keep hands, clothing and tools away from any underhood electric fan.

Caution: To help avoid personal injury or damage to the vehicle, a bent, cracked, or damaged fan blade or housing should always be replaced.

Caution: Before servicing any electrical component, the ignition and start switch must be in the OFF or LOCK position and all electrical loads must be OFF, unless instructed otherwise in these procedures. If a tool or equipment could easily come in contact with a live exposed electrical terminal, also disconnect the negative battery cable. Failure to follow these precautions may cause personal injury and/or damage to the vehicle or its components.

1. Remove the fan shroud assembly from the vehicle.

Important: Hold the fan blade to prevent rotation.

2. Using GE-47827 , or a six point socket, turn the fan motor drive plate in the opposite direction of the arrow stamped on the fan blade.
3. Remove and discard the fan blade.
Notice: Failure to tape off all of the entry points to the cooling fan motor will allow debris to enter and damage the motor.

Important: When reusing the fan motor tape off the front and rear entry points of the fan motor before drilling the rivets.

4. Center punch each of the rivets (1) from the rear of the motor.
5. Drill the head of the rivets (1) from the fan motor using a 6.35 mm (0.25 in) drill bit.
6. Tap the rivets out of the fan shroud.
7. Remove the fan motor from the fan shroud.

Important: Blow off any excess debris from the fan motor.

8. Remove the tape covering the entry points from the fan motor.

Check out the diagrams (Below). Please let us know what happens.