What's the pressure rating on the new cores? Originally, you would have had a "zero-pressure" system with the vent tube located in the top of the upper radiator tank and a simple radiator cap without a pressure spring in it.. If the recore included a new filler neck intended for a pressure cap, you could be running any of several pressure-rated caps that could raise the boiling point of the coolant. Either way, 180 is a good figure. The thermostat sets the MINIMUM coolant temperature- - - -the size of the radiator, the airflow across it, and the flow rate of the water pump will establish the maximum temp. A non-pressurized system will boil somewhere near 212 degrees, depending on altitude, and each pound of pressure raises the boiling point 3 degrees. A 15 lb. pressure cap raises the boiling point at sea level to 257 degrees. If the coolant isn't boiling the engine is NOT overheating!
Jerry