Symptom of Bad Fan Clutch?

[Krem]

so as I was taking my car to get repaired last week, I was sitting at a red light waiting for the left arrow to turn green and watched my temp gauge go from middle to prob 85-90% (just below the red hash for hot temp). This was as high as it got as when the light turned green and I accelerated, a quarter of a block later, the temp dropped back to dead middle of the guage (fell in a matter of seconds, as if I shut the car off)

After getting the car back, I was told I need to address the fan clutch as it's going bad. Sat. night as I was omw to pickup gf from work, again I was waiting at a (different) left arrow... waiting for the green, I see the temp spike in the same manner as before... sure enough, just like before, once I started driving away, the temp dropped back down.

Could this be the fan clutch failing and no air circulation past the radiator? causing it to cool down once I drive and push air across the radiator again? or does this sound like it could be something else specific?