Car overheats when I accelerate too hard and levels down when in motion. Fan is running, coolant is filled and no leaks. Is this the coolant system which needs replaced or the heads?
there are a couple of options no one else touched on, so i'll give it a go. Before buying a radiator, I would simply try changing the thermostat. They are about $10 at the most. Make sure you install it correctly. When they get old, they can "stick" where they will inconsistently open at the correct temp. Keeping cool at speed does imply the fan isn't working properly though, because it is really only useful when idling. Another option to consider is that your sending unit is malfunctioning.