2004 Mitsubishi Endeavor Radiator fan

The fans work fine until I turn the ignition off. Then, about twenty seconds later, they turn on and stay on. Something is turning activating the fan control relay. The relay is working properly - checked that. The fan will stay on even when the engine is completely cold.

If your answer fixes this problem, you can bet I will send you a twenty buck donation. I am currently living in the Republic of Panama, and there is no shop here qualified to fix this problem. They usually just cause more.