Temperature gage says car is overheating. on 2002 Chevrolet Impala

Not over heating...cold to touch. Replaced thermastat, fan,and the waterpump. Cold air comes out of the vents.

2 answers
ck water level and test temp sensor for gauge. if you unplug it the gauge should go to cold if sender is bad
Which engine is in the car? I think you have an engine problem instead of gauge trouble! I hope i am wrong.
On second thought never mind about the eng. size!
Good luck.