If the upper radiator hose is getting hot then the t-stat is probably working. If the upper hose is hot and radiator is not then the radiator is probably clogged. Yes the t-stat is an enormous PITA so its not something you just change out on a guess.
You do want to worry about the air. You should have a couple of bleeder screws to work with, though that system should actually bleed itself of air given the overflow design.
But the cool radiator is a pretty big top off. Don’t be afraid to change over from DexCool. I have an '00 Silhouette that’s been on universal coolant very happily for a couple of years & 20K miles or so.