The problem is related to the computer sending a ground signal to the cooling fans. I just fixed my daughter's 2003 Grand Am GT. The problem is what looks like a relay mounted to the driver's side fender wall. It's located directly across from the air filter assembly. Pontiac has located this device there and all your major grounds join here. The mounting plate attached to it becomes corroded which interferes with the grounding signal from the computer to turn on the cooling fans. The bolt that held it in place was actually so rusty that the head of the bolt had broken off as I removed it. I used a circular wire brush attached to my drill to remove the corrosion from the back plate. Used the same brush to create a new bare metal spot on the fender and a self taping screw to reattach it. No more over heating from there on, Fans triggered and varied speed as they should.