I find the word "air-conditioner" quite clumsy. I wonder if there exists a simpler word meaning the same thing.
Informally, an air conditioner is often referred to as simply the air:
The AC would work in these sentences as well:
Talking about air conditioning in general, AC without an article works:
I'm from Illinois, and these recommendations reflect the English I grew up speaking. I don't know whether or not people say the air everywhere with this meaning.
I would personally not say airco, aircon, or aircond, as they all sound a bit clumsy to me.