Which yellow light do you get? If it has a picture of an engine on it, you haven't disconnected the sender but another sensor on the engine that links to the ECU.
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Unfortunately I don't have any info for the 3SFE, however, I will take a look at my Parent's RAV4 tomorrow which has that engine and see if I can find the sender.
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To test the gauge, you will need to remove the dash
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(take all of the wire out and withdraw it from the car!), locate the two input terminals, and connect a 9 volt battery accross them.
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If the gauge begins to move, it is ok.
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If it doesn't, it is broken.
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Assuming the gauge works, I would get a new sender and see if this fixes it.
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If it doesn't you probably have a wiring fault, and will need to check/rewire the circuit.
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The reason why both the intercooler and radiator fans still work is because they don't run off the temp sender, the intercooler operates off the sensor in the engine lid, the radiator fan off a sender installer in the radiator at the front of the car.
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