How can I get a mildew smell out of a wool area rug?

The rug is only a few months old, 5' x 8', short pile, and mostly wool. The label says not to use a steam cleaner on it. We recently had a mildew problem in a closet (different room) and now I am noticing the underside of the rug is starting to smell musty. The is no visible mildew yet. I live near the coast and so it is usually a little damp. I can put the rug in the sun for a few hours if that might help. Any ideas?