Engine Cooling problem
2002 Mini Cooper S 4 cyl Front Wheel Drive Manual 30000 miles

The coolant is full, the oil is full, all heating and air conditioning systems are off, the engine is cool to the touch, the temperature gague is reading normal, but the engine fan will not shut off. I unplugged the relay, waited 20 seconds, and plugged it back in. it started running again. it has drained my battery.

Is it the thermostat? Is it the relay? could it be both or either?