The heater core is located inside the dash, unlikely what is causing this noise since it does not move and is not connected to anything that moves. I have seen a lot of cars that make a clicking type noise when taking off and stopping, noise coming from the wheels turned out to be loose cv axle shaft nuts. Retorqued them and the noise was gone. I would recommend you take the car back and go on a road test with the tech to make sure he/she is trying to fix the correct noise you hear.
Not just a volt tech, also a volt owner.