1997 chevy lumina 3.1 radiator

have you checked your rad. cap for pressure

When filling the coolant system you need to have the car running with radiator cap off and you can also burp the coolant hose while filling the system to remove any air. The system may be full for a while until thermostat opens and sucks the coolant out of radiator which is the perfect time to add more to top it off.

Disconnecting your negative battery cable for 10 minutes will reset the computer and shut off the light.

Sounds like a bad thermostat. I would start by replacing the thermostat. Also, make sure you have the correct mixture of antifreeze to water.

The dealer recommend GM Dex Cool Antifreeze.
But there are complaint against this type of coolant.
http://www.stevesnovasite.com/forums/archive/index.php/t-128547.html
In GM cars we replace Dex Cool with Prestone green coolant.
It's up to you. Ask before but if you decide to change the type of coolant then:
If your intention is to add coolant only, then you need:
Mix with
ANY COLOR ANTIFREEZE
ALL MAKES ALL MODELS
of cars and light trucks
add to ANY color antifreeze
PRESTONE
50/50
PREDILUTED ANTIFREEZE/COOLANT
EXTENDED LIFE up to 150000/mile 5 year protection.
DO NOT ADD WATER.

If your intention is to flush the RADIATOR (Cooling System), then you need:
Mix with
ANY COLOR ANTIFREEZE
ALL MAKES ALL MODELS
of cars and light trucks
add to ANY color antifrezze
PRESTONE
EXTENDED LIFE up to 150000/mile 5 year protection.
On the back you have to read directions:
Step 1 Drain. Step 2 Flush. Step 3 Fill.
Recommended to ad 30% to 50% volume, distilled water. If you flush the system and rinse with water you must add only 30% water to the antifreeze. There is more water trapped inside the engine compartment, because the thermostat is closed. Make sure to have a coolant density tester. When you finish one of 5 balls must sink, that indicates that you reached 50/50 strength. That means 50% Prestone and 50% Water, which will provide to your car a -34F degree FREEZE-UP Protection , and +265F degree BOILOVER protection.The next day,with a cooled engine open radiator cap, and test the strength of coolant. If not quite right, then siphon coolant from the radiator and add antifreeze, or distilled water as necessary.
Make sure to disposal the used coolant properly.

The exhaust manifold by the trans side needs to be removed to gain entry to the thermostat housings bolts

too much coolant in system,Coolant boiling away because of over heatin,Faulty radiator cap, or cracked cylinder bore or cylinder head

your door pin switch is most likely bad. it is what turns it on and off.

The overheat sounds like an air pocket in the cooling system there are two bleeder screws located on top of thermostate hosing and 1 on the metal pipe just above the water pump I believe they are 7mm. with the radiator cap off and the car running slowly open 1 bleeder at a time just crack it loose until you get a steady stream of coolant make sure to keep the level in the radiator up. be carefull coolant may be hot! when you take the oil cap off you are creating a big vacuum leak thru the PCV (positive crankcase ventalation) system this is normal for this car to surge or die.

This problem can be caused by a faulty cooling fan, lack of coolant circulation thru the radiator ( bad water pump, partially closed thermostat) or a partially clogged radiator. Make sure the radiator and condenser in front of the radiator are not full of dirt and clogging the air flow also.

Good day
if you have replace the thermostat and rad cap, after the thermostat did you let the system burb it self. there might be an air pocket in the system. you can also check the strength of the coolant if its low it won't remove the heat. also check the front of your rad the fins make sure that it's not all plugged up with dirty, bugs etc. after you get the over heating under control then we can look at the high idling
hope this helps

Cheers