Originally Posted by München
You cannot hear the electric pump, the do not have an auxillary pump to keep the water circulating
The electric water pump DEFINITELY runs sometimes after engine shutdown, and you can certainly hear it -- especially if you park somewhere quiet. This is the reason we don't need turbo timers on these cars.
To the OP... no, it shouldn't be very loud -- more of a faint whine.
Try this test: stick your key in the slot and hit the start button to activate KL15 mode (all dash lights on). Do not start the engine. Turn the heater on full hot (84+) with the blower speed in the middle. Push the gas pedal to the floor for at least 10 seconds. This activates the cooling system bleed mode. The pump will run through it's various speeds for 10-15 minutes.
If the noise you've been hearing is the coolant pump, then you'll be able to tell during the bleed procedure, as nothing else will be running to cover up the sound. If the pump sounds normal, then it probably isn't your issue.