What are the symptoms of a bad coolant temperature sensor on a oldsmoblie arura?

This answer is not specific to your vehicle, but coolant temperature sensors function the same on most types of vehicles, so if you suspect a faulty coolant sensor, then you must have a vehicle using more fuel than is normal. The most obvious check if access is possible is to put a voltmeter on the terminals and measure the voltage as the engine warms up, most give a high voltage from cold which reduces as the engine warms up.