The keg is my favorite aging vessel.
Just like with cellaring bottles, I like to keep them cooler than "room temp" - my basement is around 62-64F. But if the closet is the coolest place you've got, go for it!
Put some pressure on it to seal, then check it 24 hours later then again every month or so to make sure its holding pressure. The last thing you want is for your precious aged beverage to be exposed to air for months on end!