Depends upon whether your idiot lights have a Cold with a blue lens that lights up when you turn the ignition on. If you don't (you have only the red lens saying Hot) then that is an extra wire that you do not need. It was included because it cost too much to make two separate wire harnesses for the car. The Cold light was an option to tell you not to rev the engine unril the oil got to operating temperature for extended engine life.
There are three different temperature sending units. Standard over temp (one wire) the deluxe Hot/Cold (two wire) and the one used with a gauge that sent a continuous signal (another one wire).