DTG, Is it a steady continuance beep, or a beep, beep, beep?, I just went through the same thing. Mine was a bad low oil sensor that is in the underside of the oil tank on the motor.
It was a beep,beep, beep the continuance beep is a heat warning. If it's peeing a good stream the water pump would be ok I would think.
I would check the thermostat, maybe you could unhook the wire to it to see
if it stops beeping.
Good Luck.............crappie cowboy