It may be that your thernostatic fan clutch has leaked dry and is no longer functioning properly.
Radiator could be partially clogged.
Also, pull the new 'stat and toss it in a pan of 200 degree water and see if it opens. I have gotten bad ones before.
The water pump impeller could be spinning on the shaft, but I doubt it. If it's not leaking or making noise, it probably isn't bad.
Finally, if it only overheats at highway speeds, squeeze the lower radiator hose and see if the reinforcing spring that holds it open has rusted away. If it has, your hose may be collapsing above 1500 rpm and cutting off water flow..
Take off the radiator cap and if you see lots of bubbles in the filler neck(with the engine running), you may have a blown head gasket.