Need to look at the fans when engine is overheating. If they are not working, then there is a problem with the fan motor or the control and power circuits (sensors,wiring, relays, etc..). If they are working, then make sure the air dam in front of the car is still there, they are known for breaking off or people removing them for strange reasons. Make sure there are no air bubbles in the cooling system as they can cause all sorts of weird problems. If the cooling system is in good shape, then there is a possibility of a blown head gasket, which can cause sudden rise in coolant temp. Have the coolant tested for the presence of combustion byproducts as their presence is a sure indicator that exhaust gases are entering into the cooling system. Also make sure you have the a 50% water 50% anty freeze mix in the cooling system as this raises the boiling point of the mixture, and that the proper type of radiator cap is used as the pressure is needed as it also increases the boiling point.
You mentioned there are two fans, one in front of the other. This seems strange to me as usually they are mounted side by side or one in front of the radiator pushing air, and the other behind the radiator pulling air. In any event make sure both fans blow air into the engine compartment and not fighting each other.

 

Air dam is still in tact. You are right on there Camaro there is one fan in front of the radiator. They have the 305 coupe. So if my Moms a/c compressor is shot will I still be able to see if the fan is turning by turning on the air even though the a/c does not work? Or is the only way to test the fan is wait until the car gets hot enough to see if it comes on? My understanding is and I will double check this they are using the 50/50 mixture. Can you please tell me the easiest way to have the coolant tested? My step father bought the non vented radiator cap could this make that much of a difference where there car would over heat? I told him to buy the vented cap as someone recommened but he didnt. Thank you for your reply.

 

I don't have a wiring diagram handy for your car, but some AC systems a re set up to turn on both fans automatically as soon as the AC is switched on. Other will turn on just one fan when the AC is switched on, and then turn on the other fan as refrigerant pressure reaches a certain level (which won't happen with a bad compressor). The radiator cap for the system in your car has a double seal, one seals at the bottom of the radiator neck and the other seals the top of the neck. The bottom seal releases at 14 to 16 PSI and allows flow into the reservoir, the top seal does not open so that the coolant can be sucked back into the radiator when things cool off. This link will help.
How Car Cooling Systems Work - HowStuffWorks

 

Thank you Pete. I will look into the link you sent. I guess it cant hurt by telling them to turn on the air and see if the fan is turning. I suppose the next I can do is also have them let the car reach hot and see if the fan comes on. This one guy that my step Father met and had him replace the water pump and hose will not return my step Fathers calls or mine for that matter. The are on a fixed income and I am trying to help them the best I can although I will not be going to their house for a while I am tied up a bit with my husbands illness and it makes it tough. Thanks again.

 

One thing you should keep in mind is that usually the only thing that goes wrong is the seals around the shaft or the bearings. If the seal go bad you will notice coolant leaking around the shaft or out of the weep hole under the shaft. If the bearings go bad they will make ugly sounds and eventually allow the shaft to wobble and damage the seals. So, unless the pump is seriously leaking the engine will not overheat as long as the coolant is replaced. Also, when you top off coolant in a system with coolant recovery, it is a good idea to remove the radiator cap and fill the radiator to the top, then replace the cap and fill the catch bottle up to the low mark.