100% polyester will not shrink in the dryer.
More Info: Polyester is a manmade fabric designed to resist wrinkles, shrinking, and stretching so it is unlikely that a 100% polyester garment will shrink when washed and dried.
Polyester is often blended with other materials, such as cotton, which may make a garment more susceptible to shrinking depending on the ratio of cotton to polyester.
Source: "Selecting a Blouse, Ohio State University College of Food, Agricultural, and Environmental Sciences
What Is Polyester?
Polyester is a manufactured product, usually used as a textile, that is made from synthesized long-chain polymers. Polyester fabrics are extremely strong and durable, as well as naturally hydrophobic, making them quick to dry. Polyester is also used as a plastic. In this form, it is used to manufacture a wide variety of products such as liquid crystal displays, tarps, films, and larger items like canoes. The term polyester most often refers to polyethylene terephthalate.
How Do You Care for Polyester?
Polyester garments require very little in the way of special handling. Polyester is a synthetic material made from long strands of fibers that wear down in high heat. Polyester garments can be machine washed and dried, but it is best to do so on the lowest temperature setting your washer and dryer allow. Never use chlorine-based bleaches on polyester, as this can also break down the fabric. The material resists wrinkling, but if your garment must be ironed, be sure to use the lowest setting.