If you don't exhaust the heat outside the room in which you keep this chiller, you will end up fighting temps. That is, the room will get warmer, and thus the chiller will have to fight harder to keep up. The more it runs, the greater the heat it produces, which will increase ambient temps in the room.
Think about it this way: when you pull heat out of a fermenter, it has to go somewhere. The air conditioner exhausts that heat to the outside of a house. But if you keep that in your little room, it'll just warm up the room.
Now, if you use this just to maintain ferm temps in, say, the 60s, this probably won't be a huge issue. And if you have a very cool room (it's a wine celler, cement walls--lots of thermal mass there to absorb heat), then you may be OK.
But I'd question what happens if you try to crash that fermenter to, say, 38 degrees. That's about as low as mine goes, and the chiller runs a lot to do that--and it's a Penguin chiller, not an air conditioner not designed originally to chill. In other words, it's pumping out heat, both from the heat pulled out of the fermenter, and the heat generated by the running of the chiller.
One other thing: it's a wine celler. Do you want your wine to rise in temperature too?
I'm hoping someone else who has this kind of thing in an enclosed space can weigh in as to how much rise they see. The saving grace might be the cement walls, but even then, over a 3-4 day period, things are going to warm up in there.
