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.
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.
I would suggest a new set of plug wires.
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
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.
You are not giving enough information to get a reasonable answer. It's like asking why it won't start. Any, and I mean any, detail would help. Are we talking about the engine cooling system? What are the symptoms that bring you to the conclusion it is overheating? Have you checked the coolant level? What year and size engine? Does it overheat only when stressing the engine, like climbing hills? Does it overheat only in traffic and okay on the highway? Does it overheat when the car is idling? Has the head gasket ever been replaced?