On a trad system you can jumper the fan direct to the battery to check if its bust. If you connect it up the wrong way it'll run backwards, telling you you connected it up the wrong way.
You can probably do this even on an ECU controlled system, though I have no experience of them and don't much want any.
On a trad system, IF the fan works, check the fan relay. If its OK, check the thermostatic switch that controls the relay. Acdually checking it is a bit tricky, involving fiddling around with hot water and multimeters and probably burning yourself, but you can substitute a paper clip to short it out (since it makes a circuit when hot) and see if that makes the fan go.
If these are all OK, its the wiring between them.
But are you sure your car IS actually overheating? Has there been any work done that could have created air pockets, which can mimick overheating? This could explain why your temp gauge shows normal, or (since you have lost coolant) there may be an air pocket next to the sensor.
Or its bust
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