OK ... if the fan is coming on even when the engine is cold, you got one of three conditions:
1) Defective (shorted) temp sensor
2) Defective cooling fan relay
3) Defective PCM
With the key OFF, pull the cooling fan relay, and tap it vigorously on your knuckles. Now plug it back in, and turn the key to ON, but do not start the car. If you hear a click from the relay, and the fan starts, best chance is that the temp sensor is shorted, and needs replacing. Verify this by turning the key to OFF, disconnecting the temp sensor connector, and measure the resistance of the temp sensor. Zero ohms signals a bad sensor.