I had to replace the water pump this weekend. After it was replaced, the engine still wanted to overheat and would only blow cold air. I replaced the thermostat, hoping that would address the issue, but still the same. I'm going to check one more time to make sure the coolant is topped off, but are there any ideas if that looks ok?

It sounds as if you may still have air trapped in the system. Try this procedure from techinfo and see if it helps.
http://www.bonnevilleclub.com/forum/...=article&k=100

My problem is solved! To be honest, I did not fully follow the steps listed, as I was unsure about drilling a port hole in the flange. Bypassing that step, I followed the other steps and all is well. Thanks for the quick response and the help.

Hey man, how are you. I'm having the same problem with my car overheating, a 2001 Bonneville. For some reason I can't access the link provided here. Could you tell me what the steps you followed are? Thanks.

There is a bleeder valve n top of the T-Stat housing. Open that to bleed out air. Also, when the system is warm, you can squeeze the upper radiator hose a few times to help push fluid/air through the system. Top off you coolant reservoir after bleeding.

You may need to replace your T-Stat. Here'* a great How To for doing just that https://www.gmforum.com/t278803/