cooling problems....
This is happened to me many times when I've done coolant or thermo changes on my 99 and on my 02. With the radiator cap off idling, it'll push coolant out the radiator and overheat. You will need to have the radiator cap on so the system will build pressure and air in the system will get forced out into the overflow tank. With everything buttoned up, disconnect the throttle body coolant hose and fill the radiator till coolant comes out that hose, then reconnect and fill the radiator as full as possible and install radiator cap.
Have the overflow coolant tank midway full and run the car up to temp at idle. you will need to let the engine cool, or use a towel and be carefull when removing the radiator cap. It might take you 2-3 times refilling the radiator as air pushes out the system and fluid level drops in the radiator, it should burp air out into the overflow tank and pull coolant back in from overflow tank but you need the system nearly full to begin with for that to work.
i doubt the thermostat is bad, but you never know. it will however not matter if you do not have a radiator cap on that is functioning and allowing the system to build pressure.
you might also have a faulty radiator cap, you'll know that if when you try to remove it when the car is hot and coolant wants to blow out and burn you- if that does not happen then good chance the cap isn't sealing. don't burn yourself obviously.
other than that, only thing left is water pump and if it's turning and not leaking then it's most likely working. with engine fast idle and hot with system under pressure, you should be able to squeeze upper radiator hose by hand and feel coolant surge, if you don't than start looking into why coolant isn't being pumped... again you need a good radiator cap and system under pressure.
Got the car back to the apt and let it idle, not going above 230 again. (seemed i had an air pocket and things started to work itself out on the drive, there was fluid in the hoses and i had pressure again.) i carefully removed the cap and level was high and pretty hot.
checked my fans and one was on but the other wasnt, i took my starter relay(same relay as the fans) and swapped it in with the fan relays and the other came back on.
so i just got back from gm with the new relay and also a coolant temp sensor (just to be sure)

