1996 Subaru Outback Repair Question
Start by checking the fuses under the hood. A tight fan motor will eventually cause a fuse to blow. If the fuses are okay, it's possible the coolant temperature sensor is defective. On some models unplugging it while the engine is running will cause the Engine Computer to turn the fans on as a precaution because it doesn't know the actual engine temperature.
Also look at the fan relay(s). Try swapping it with a different one like it. If you can bypass the relay or pop the cover off and squeeze the contact and the fan still doesn't tun, the fan motor could be open. That's usually due to worn brushes, and often spinning it a little by hand will get it going for a little while.
Where is the coolant temp sensor found at on the car?
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The sensor will always be near or on the thermostat housing. Most cars in the '80s and '90s had two, a single-wire sensor for the dash gauge and a two-wire sensor for the Engine Computer.
A different approach is to find a mechanic with a scanner that can access your Engine Computer and display live data. It will show the temperature the computer is seeing from its sensor, and it will show when the radiator fan is commanded on. The more advanced scanners are "bidirectional", meaning you can turn things on and off by selecting from various menus. When you select "radiator fan", it typically will make the relay click on and off about once per second. That lets you do electrical testing in the high-power switched circuit. If there's no voltage anywhere in that circuit, suspect a blown fuse. If you DO have voltage all the way to the motor, either the motor or the ground circuit is bad.
I have changed the coolant temp sensor and car is still overheating at a stand still and the fans still not coming on
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Testing is always preferred over just changing parts. If the sensor is bad, you can usually verify that by just unplugging it. That should make the fan run. (See my correction at the end).
What I would do next is to look for the fan relay under the hood. That will let you instantly split the circuit in half to see which half works. I couldn't find a listing for an Outback in '96 so I used a Legacy. Here's a photo of what the relay looks like from rockauto.com. I added the two red arrows to show the switch contact terminals. You will likely find those two wires are fatter than the other two. You can jump those two fat wires together with a stretched-out cotter pin or piece of wire. A stretched-out paper clip is my favorite tool but they can get hot.
You can also pry the cover off the relay, then squeeze the contact arm to turn it on. Either way, if the fan runs, it's the low-current control side that has the problem. More commonly the fan will not run and the high-current side is at fault. Then you have to test for voltage on one of those two fat wires, (red arrows). If one has voltage, the fan motor, the wire going to it, or the ground wire is bad. If neither has voltage, a fuse or fuse link wire is burned open and most likely it's because the motor is tight.
I also noticed they listed a "Radiator Fan Switch" which is different than the two-wire computer sensor. It appears to me the Engine Computer is not involved with the fan, just a temperature switch. Unplugging the connector and grounding that wire should turn on the relay and fan motor. If it does, that switch is defective.