What if you rent a house and the converted garage's AC (this is a forced air unit) isn't cooling that room enough for anyone to inhabit it or sleep in it? If you rented a 3bd home and now it's unusable space to 2bd due to extreme heat? They prop management said they would have an AC guy look to see if something could be done, but haven't as of yet. If that AC guy says nothing can be done- can I break the lease being I can't use the space?

Something can be done. It just might cost too much to be worth it.

How long have you been renting the house? Was the problem not apparent when you rented it?

Just a couple of months and was out of state for the first month so didn't know. And no it wasn't apparent when I rented it