Hey, good idea. I thought about doing this once. My closet is a little too far away really, but it is always cooler than the rest of the place, especially in the winter. No heat in there, so it is about 10 C colder right now.
Now, however I am working on a custom case build that I will want to show off, so hiding in the closet is out of the question. The new case should have better cooling as well, so two birds shall be dealt with.
Let us know how the cooling goes over time. It will be usefull info. It might be nice to have a server in the closet with a wireless network to a small desktop PC.
Good luck.