Turn on A/C and see if the fan is running. It should run continually with the A/C on. If it is not, check the fuse, or fan motor itself. If it does run with the A/C on and no any other way, then check the thermal relay.
Sounds like a fan or fan shroud problem, but you could also be dealing with a plugged radiator, undersize radiator, or thermostat problem.
Either the fan is no good or the heat sensor in your radiator, that turns the fan on is not working!!
I check radiator fan, and relays and they are good, what can be a problem when my car reaches temperature to open termostat radiator fan does not work
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.
There are a few ways you could make your radiator fan turn on. You could fix the wiring for example.
in the pipes going to the radiator or you need a new radiator
check the thermostat or the fan motor could be the problem or a leak in radiator. just a thought
Dirty or plugged radiator Water pump Defective radiator cap Thermostat Cooling fan not operating hoses collapsing
Stuck Thermostat, clogged radiator, defective water pump, defective fan, fan relay, or blown fuse. A defective radiator cap will in some instances make the car to appear to be overheating.
Problem with the temp sensor.
Most likely it is a bad thermostat. The switch on the radiator fan could also have failed.
It could be your radiator fan.