My 2001 LS 3.9L overheated about 2months ago. it pegged the temp gauge, and the reduced power light came on. I pulled over and let it cool about 5-10minutes.When I started it again the gauge was at the halfway mark, where it is normally.
Thinking it might be the hyd.fan, I got on the interstate and drove at 70-75mph hoping the fast air flow would keep it cool. It did for a couple of miles,then started gettin hot again, but would cool down on its own.
Ever since then it would get hot about twice a week, no matter where or how I was driving.Now it gets hot about every time I drive it! I tryed it with or without the A/C. No change, it seemed to get hot when it wanted to!
I found that when it showed that it was hot, I could pull over turn it off wait a second then restart it. The gauge would go to the half way mark, and all seemed ok. Sometimes it would remain cool, and sometimes it would show hot again, and I would pull over and restart again.
It acted like the thermostat wasn't opening, but as soon as I restarted it it would cool down!
After reading one of the posts in this forum about how over loaded the electic system is in these cars I started wondering if the battery could be causing false sensor readings!
Someone had installed a smaller 400CCA 500CA battery instead of the larger battery that it should have.(650-750CCA). Idid a load test on the small battery and it dropped like a rock!
I bought the right battery, which was hard to find, and installed it. I also checked the ground connections, and the main pos. to the fuse box, and cleaned the terminals.
It's been 3 days since I installed the right battery, and it hasn't gotten hot once!
I never would have thought the battery might be why the car was overheating! But so far It hasn't gotten hot. I will keep you updated as I drive the car more..

As sporadic as the gauge was acting, the weak battery may have been playing games with the coolant temperature sensor circuit.

Interesting post, keep us updated as you get a few more miles in.

-Rod