hot air comes out the vent of the middle?

Hello, I'm Danny.

Here is the information you requested. It sounds like you are having an issue with the auxiliary mode actuator which is not opening to provide cold air. Here is a tutorial showing how to replace a blend door actuator which is similar:

https://www.2carpros.com/articles/replace-blend-door-motor

I've attached picture steps below on how to replace the auxiliary mode actuator on your Cadillac. Hope this helps and thanks for using 2CarPros.