Yes you want to bleed it as JW said, air pockets can cause overheating, and issues with the coolant, especially if you used DexCool again.
When I bled mine I drilled a 3/32" hole inside the gasket area of the stat, at what was going to be the 12 o'clock position of the thermostat when installed, then I just squeezed the upper rad hose a few times, and added more coolant after I was sure all of the air was removed.
To be extra sure I started the car and let it run for about a minute, since you do not have a hole drilled into your maybe 2 minutes of so, you want to start bleeding it as soon as the thermostat opens, be careful though as the coolant will be hot, and could easily burn you, I'd wear gloves, twist open the bleeder screw till you see coolant, and air bubbles coming out, as soon as you see a straight stream of coolant you can tighten the screw, after that let the system cool off for around 30 minutes or so, then pop the rad cap off and top it off if the level has dropped.
I did this, and then the next day I repeated the process to be sure I had no air in the system.
Many will do it in a bit simpler method, but this is the way I chose to do mine, and I have not had an issue with it at all, and it has been 2 years plus..
2006 Pontiac Grand Prix GT with SC
1996 Buick Park Ave NA