My car was overheating so I got my mechanic.

Hi my car was overheating so I got my mechanic to put new radiator in and it stopped but than about a month later it started overheating again but only when I am not moving eg stopped at traffic lights I took it back to him and he said he won't fix it my friend said it might be the water pump should I just buy the water pump and see what happens or should I just take it to another mechanic I also thought it could be a radiator hose but not sure