Hi when the clutch fan screw up, you can rev your car up to say 5000rpm and the fan will only spin fast enough to support around 3000rpm due to the oil inside the clutch fan die, it doesn't expand therfore fan doesn't engage at %100 as it should be, another word is yes it work but its' slipping therfore it will heat up eventually.
You can also test it out when you just come back from somewhere switch the inigtion off, try to spin the fan with your hand and see if it move or not. If it move then it really is on its way out cos' the engine still hot, oil expand and it should not move. ( Correct me if i'm wrong )