You say you bled the cooling system, but is the air out of the heater core????
I remember when i did a heater core change, and when i filled it up, ran it for 10 mins. Temp guage kept running funny, and I figured it might have air in the core. Put the front on an elevated surface, (a set of car ramps did the trick) and the air should come out of the core, and you might hear some bubbling. I know as soon as I got the car on those ramps, I heard it, lol.
Might be something to consider?
2009 Pontiac Vibe AWD 2.4
1993 Buick Park Avenue 3800
1984 Chevrolet Citation 2.5 liter four.