Sorry, I'm not that familiar with your model. I thought you center console looked like this:
Anyway, I'm having a little trouble verifying the details, but I think the climate controls are built into the bezel (the part surrounding the screen), but not connected to the head unit (HU for short). Don't hold me to this, but it looks like the HU is mounted behind the display screen, which in turn is mounted to the bezel with a couple of brackets.
What does that mean? Well, IF I'm correct it means the HU and screen can be removed, and you'll still have climate control. The problem that you then have is that you will need to find an aftermarket HU that fits that bezel opening.
Auto climate control. You set a specified temperature, say 72 degrees, and the system will automatically switch between heat and AC to maintain that temperature. Going by your picture, your climate control is manual.