Could this part be the problem?
They are probably recommending an engine wiring harness replacement.
P2185 is a circuit fault that involves the wiring harness.
I’ve had others look at the wires and they say they’re fine so it’s hard on who to really believe
The wiring circuit should be tested using an ohm meter. The circuit can be tested at the computer connector to verify proper resistance from the computer to the sensor. Did the others who looked at the wiring test for an open circuit?
In most cases damaged wiring can be repaired. Did they find rodent damage? When a repair shop gives a $2,000 estimate, it usually means they don’t want to deal with the problem, you’ll need to find someone else to perform the repair.
After the faults are erased, does the check engine light illuminate immediately after starting the engine? If it does, this indicates a continuous problem with the circuit and should be easy to verify. If it takes several days before the check engine light comes on, this would indicate an intermittent problem and might be difficult to locate.
Yes, but there’s a hundred other parts that could also be the cause. Relays are usually pretty robust so that particular part seems an unlikely culprit, unless it the exterior is melted or discolored . Suggest instead to focus on getting a proper diagnosis. @Nevada_545 gives some excellent ideas how to proceed above.
The dashboard coolant temp gauge rising even though the P-code is suggesting the coolant temp sensor circuit is faulty is a very important clue. Be sure to tell your mechanics about that.