No matter what you used, it probably still wouldn't work if it was KO'ed. Try using the electronic odometer trick
to see what your temperature is. You don't have to turn on the engine- only turn the key to ON in order to set the odometer to test mode. Once set, it will remain in test mode until you turn the key OFF, so you can start and see your temp climb if it does.
On this car, with the Zetec engine, there are 2 things that typically happen to make the fans not work. The first is the engine cooling fan resistor that goes out, and the second is the cooling fan plug-in connector that you would've probably already noticed as being melted.
I'll bet your fans come on as your engine temp reaches 116 C. That means that the low speed resistor is out. You can fix this by replacing the resistor, or you can make a joint on the hot wires to the fans so that your fans will come on high speed when either circuit is turned on.
What was written earlier is correct. If your temp gauge is showing temperature, then your temp sensor is not bad- maybe. It might be reading incorrectly, but the only way to diagnose that is to get an infrared thermometer, then use the electronic odometer trick to watch your engine temp. I would shoot the infrared thermometer on the upper radiator hose near the thermostat, and I would expect about a 5 C difference. Also while you're driving look for wacky jumps or drops in temp that would indicate a failed temp sensor.