If the smoke is coming from the electric fan itself, then it needs replacing. It could be the smoke is steam that the fan is drawing from the radiator, and you have a coolant leak at the radiator.
Sounds like a sticking thermostat. When you say "the engine isn't hot", you mean "the radiator isn't hot", right? Because if the temperature gauge says overheating, your engine ishot
Blown head gasket.
Consider replacing your radiator cap . .
look for antifreeze coming out of the radiator as the engine warms up after a cold start.
Check your heater hoses, that's where the water ciruclates into the heater from the water pump.
appearance, reappearance, coming, replacement, reaction
heater core needs replacement
That smoke is steam. You have a leak in the radiator or a hose. Take it to a mechanic.
The coolant is pumped from the thermostat housing into the top of the radiator but not until the thermostat opens.
because there is a crack in you engine and its runing over in to it
you should find it attached to the radiator & the water pump. if it is missing, that's where you should put the new one. radiator at the front of the vehicle, engine behind it, water pump on front of engine, with hose, or short metal tube coming out of the bottom of it. the radiator will also have a hose or short metal tube coming out of the bottom of it also,(the radiator should also have another hose coming from it at the top)