The garage will not get as hot as the normal heat in a clothes dryer. As others have pointed out, it's the humidity and any possibility of critters that cause some concern. If there is a lot of wildlife in the area, particularly if you have pet food in the garage, bugs or rodents might turn up there that you'd never see in your house. Plastic bins with tight lids would be my preferred way of storing fabric for a few weeks. Vacuumed plastic bags are costly and are too easily gnawed through. Besides, vacuuming them would be a time-consuming extra step for you.
We live in an area with high humidity and lots of wildlife, and the garage would not work for me. When we first moved here in 1974 we put boxes of books and old pictures in the attic, a terrible mistake!