I believe the tstat should be a 195*f, as most are. I could be wrong... some cars require a 185 or 205*f stat. As I stated previously mine runs 175 down the road in the winter(on the scanner not gauge,) I believe mine is staying open a crack... I digress... Long post to follow, be warned
When you pulled the stat, did it have the small air bypass valve with the bobbly-thing in it? Hopefully, yours had one and it was pointed in an orientation to help remove air (or other gasses.) Otherwise, air removal can be facilitated by drilling a 1/32" hole about 1/8" from the outer edge (or wherever convenient to allow air to pass around.) some race engine builders feel it's dangerous to drive without a stat, as this causes too much flow. I don't know if that's true or not, but I wouldn't let anyone catch me do that if I was trying to get an engine warrantied.
I've had success bleeding difficult cooling systems by using a vacuum refill kit, although others have said this vehicle isn't that difficult (haven't done mine or another Aveo yet-- but soon.) If you use a vacuum refill kit, please make sure you do it when the engine is Cold.
How soon after stopping does the temp go back down? I knew I had a problem with my intrepid because the fans would be on but the air coming out of them from the radiator was cool even though both hoses were hot. That would lead me to believe there is either a lack of coolant flow thru the radiator or gasses trapped in there.
I block tested my intrepid several times... People behind would flash their lights sometimes (getting splattered with coolant or smelling it?) but I never saw a color change in the dye tester. I even took the spark plugs out one by one and fed the cylinders air with the radiator cap off and nothing... I replaced a radiator, fans, tstat, and lower intake gaskets... still ate coolant. I am never a parts thrower where I work, but this thing had me at my wits end. Finally, one day I heard the mighty kaa-chunk of the starter kicking back. Pulled the plugs one by one and found the offending cylinder was full of coolant. pulled the plug out every morning and cranked it to relieve that cylinder. put it back in and Drove it like that every day for 6 months and junked it.
I don't wish that fate upon anyone, it's very frustrating as you can see. In order for heat transfer to occur, one needs pressure, surface contact, flow, and convection. I'm not sure if the fans go off above a certain speed, but I wonder if the A/C condenser is getting too hot or there is not enough airflow through both heat exchangers. On my best customers, I blow backwards with gentle compressed air or water to remove dirt and fuzz. Hands work good for determining hot and cold spots, non contact temp guns are a little better-- but those too have their limitations. I still gauge temps by hand at times and I believe 210 and over gives you a "ye-OW!" feeling. 180-190 gives you an "ow" and I think you get the rest. Unless a cold beverage has chilled your hand, then you can expect sensations to be exaggerated.
HTHY, good luck
Respectfully-- The Krusty Mechanic