Place your polyester piece into the large plastic bag that comes with a home dry-cleaning kit.
Open one of the dryer sheets from the kit and unfold it. Place in the plastic bag with the polyester piece and seal the bag.
Place the bag into your dryer machine.
Set the dryer to the "tumble" setting and allow the machine to run for 10 minutes. The heat should be set to high unless otherwise instructed in your specific home dry-cleaning kit's instructions.
Remove the bag from the dryer and remove the polyester piece from the bag.
Shake the polyester piece out and place it on a hanger immediately to ensure that no wrinkles set in.