You say happens with motor OFF and when motor is on, while moving and stopped. One thing I can say is, it is NOT, Motor related or Radiator. With the motor off nothing attached to it will make noise except an over heated cooling system, hiss or gurgle.

I will guaranty that is caused by something you are sure it can't be caused by.

 

Ok. Did some unorthodox drivability diagnosing and found it is in fact the wheel bearing. the coolant / overheating deal is a seperate issue. Im guessing thermostat seized only opening due to pressures created by the pump itself. But i appreciate everyones help.