01' V8 LS Temporary Overheat

For the past several months after starting up the car, within a little while of warming up, the temp gauge will shoot up in conjunction with the throttle. As long as I stay on the gas, it will continue to rise until it gets to hot and I get the reduced engine power message, oil light, etc. Then just like that after climibing all the way up, it will instantly drop right back down to normal and it runs fine. Of course it is accompanied by the high pitched whining noise from the fan and how loud it is directly correlates with hitting the throttle. It may do it all over again if I come into a town and slow/stop and accelerate again. Wondering if anyone has any suggestions where to look first? (coolant levels show fine in the resovior) Thanks

Not that they are related but I also get the batterly light/check charging system message intermittenly after start up for a little while before it goes away. Battery is pretty new.

You have a small leak in the cooling system that is letting air in. This lets the heads overheat. The plastic cooling system parts (including the degas bottle) are well know to get very small cracks over time.

The "battery" light is for the alternator only. It does not indicate that the battery is bad (or good). It only indicates that the alternator can't keep up with demand. Most likely, the brushes in the alternator are worn out.