I store fabrics in our unheated garage, and have for at least 3 years. No problems so far. Of course, I visit the fabrics every time I go out in my car, and even more when I'm imagining a quilt.
I'm more worried about mice getting into the fabrics than heat/cold damage. However, that could happen inside the house or in the garage. So far we have had no mice/rodent problems, though.