Replacing expensive parts is never a good way to diagnose a problem.

Diagnosing a failing fan clutch is easy. Let the engine running until it is above normal operating temperature (not to hot). Stop the engine with someone watching the fan. If is does not stop immediately if the engine stops it is defective (or the bold that attaches the fan to the clutch is loose).

Never stick something in a running fan, that is very dangerous, the fan will break and parts will fly out.

You may also check if the fan cowl (the plastic thing around the fan) is properly seated, if air can enter between the radiator and the cowl cooling is dramatically reduced.
If you do not know the history of the car check also for the less obvious mistakes in the past, like mounting the fan the wrong way. If it tries to blow the air towards the front cooling will not be as effective.