Copper wire can turn black and still function, though it's not a desirable situation for sure. The black appearance can be caused by components of the insulation deteriorating and migrating and acting on it, causing oxidation or other chemical reaction over long periods of time. Exposure to temperature extremes and other environmental factors doesn't help either.

You can replace parts of that harness with copper wire. The sensor is a thermistor so it's not sensitive to wire type like thermocouples can be. However before you do that, you should check end-to-end continuity with an ohmmeter to prove that the wire is actually the problem.

Considering the 'dry circuit' nature of the thermistor, I'd suspect a corroded connector somewhere before the wire itself. With the low currents and voltages in the circuit, it doesn't take much deterioration at all in a connection to cause trouble. And we're talking about something that's 16-17 years old, so this kind of problem should be expected.