335i Water Pump

My gearbox was overheating as stated in a previous thread. The car was send to BMW today and they say it is the water pump. My question is how can it be the water pump if the engine is not overheating? They basically say it is now a process of elimination to find the fault. Can someone please tell me if you had the same experience before or know anything about this. The first quote is R13500 to replace the water pump.

Thanks
Willem