How read signal from car oil temperature sensor?

Can you first measure the voltage across your transducer with a DMM and tell us what the value is at cold and hot?

Assuming you have done this and the value doesn't go above 5V, you can feed it directly into an analog input on your Arduino. Your question assumed there was no noise. If this is the case, you are good to go. If it turns out that your signal:noise ratio is unacceptable then you will need to do something else. Conditioning the signal with one of the instrumentation amplifiers I mentioned earlier is one of the things you can do.