Check to see if the area between the radiator and the ac condensor is plugged up with whatever. It may be hard to see without taking the radiator out but it could be loaded with leaves or what have you.
The radiator cooling fan is most likely not working.
If the electric cooling fan(s) are not coming on that may be the problem.
I would suggest a new set of plug wires.
If the coolant is low ( watch for leaks )it will act as you say. Fill it up , leave rad cap off for 5 minutes while idling to bleed air, and try it.
If the Chevy Celebrity radiator is smaller that the Saturn radiator it might well overheat from not enough cooling capacity. If the Chevy Celebrity radiator is the same size or larger than the Saturn radiator I would think it would not over heat.
Check to make sure the fan clutch is engaging.
You need to check your cooling fans and be sure that they come on at 232-235 degrees. They should shut off at 195-200 degrees.
check your thermostat
Blown Head Gasket or Bad Cylinder Head
one of the main reasons an engine runs on or diesels can be related to the fact that it is idling too fast. Set the idling down and see if this imporoves
Lots of reasons, but mine was the fuel pump was bad. It would overheat after driving maybe 15 minutes, then I would let the car stop for an hour or two and it would start back up.
I would suspect a vacuum leak. If the car is over 10 years old, I would recommend you replace all vacuum hoses under the hood. Do them one at a time as to not get confused.