I was surprised when my wife came home and turned on the air coniditioner.
Is she not allowed to touch the AC?
It's not that she isn't allowed but we're separated now, she's the only person with a key and the air was randomly turned on when I got home.
That's some strange behavior from your wife and it makes sense that you're confused about it. If you're separated, you should have rules set up for each other to keep things civil.
I should fucking deck her in the face.
No you definitely should not. Get control over your emotions, this is nothing to get violent over. Communicate to your wife about your boundaries and see that starting with the AC is the first in many steps to repairing your marriage.