You need to start the vehicle cold and feel the upper radiator hose. If it gets hard before the engine gets hot you likely have a blown head gasket. A heater core will only cause an overheat if it leaks and runs the coolant low. How long has it been since you replaced the water pump and thermostat?

Here are a couple things you should check:
1) Make sure that your cooling fans are working. When you start your car, let it get fully warmed up and open your hood and listen for your fans to come on. Don't let it overheat. They should come on after the guage starts looking hotter than normal. If they do not you probably have a fuse, relay, or fan motor that has gone bad...these are just the most likely causes.
2) Also check that all of your shrouds and air dams are in place. If they are not then there may not be enough air going through the radiator.

If your coolant is always full and your car never loses any coolant then it cannot be leaking. Keep in mind however that sometimes your radiator will look full when it is actually not.

I hope this has helped. Please let me know if there is anything else I can do.

More than likely you have a failed intake manifold gasket. Very common on this engine. If you look down from the top sometimes you will see coolant puddled below that area. If the heater core was leaking you would get leakage on the pass side from the AC evaporator drain. Check your oil to make sure it doesn't look milky also, since they can leak internally. A pressure test will verify the leak at the manifold, and it will need to be replaced if leaking.