Im having issues with my 2003 Monte Carlo the temperature gauge while driving after a few minutes will shoot up to overheating then once you turn the car off for a little bit and you turn it back on after a couple minutes it's fine but you got to get to where you got to go or it shoots right back up I just replaced the thermostat and what else could it be if this does not work. Out of opinions

 

This is most likely the upper and or the lower intake manifold gaskets.
I kind of questioned this my self a few years a go and I have a 2006 Pontiac torrent and it has the 3400 motor.
I had the gaskets replaced and it took care of the problem there have been several posts about that issue here and folks with the 3800 motor had the same issue.
Before I couldn't make it thru a fast food drive thru without it getting to hot and the Fans kicking on.
However make sure that after these maintenance efforts you have performed that you made sure there were no bubbles in the cooling system and it was properly bled.
When you check the coolant level on the recovery reservoir is it in the proper line, for Cold and Hot? Sometimes coolant level is just lower than it should be.

 

Intake gaskets justvhad that same problem