Cascades to Coast

kinetic energy

If according to the kinetic theory of matter, molecules move more and spread out when given heat/energy, why does cotton shrink in the dryer?

Cotton is mainly cellulose, which is a long chain polymer with alcohol (OH) groups all along the edges of the molecules. These interact with water well (but don't dissolve), and when dried, they interact strongly with one another. That's the basic chemistry. My guess on the shrinkage question is as follows.
When cotton threads are generated, they are pulled lengthwise to make convenient fibers. This may not be the best orientation of the individual molecules. So when they are heated, they gain kinetic energy (moving around a lot more), which gives them the opportunity to find a more stable arrangement. That more stable arrangement is not likely to be in a straight fiber, so some wrinkling as well as shrinkage occurs on the observable scale.