Put the curtains in the dryer. Toss in the wet washcloth. Tumble dry on low heat for 10 to 15 minutes. Remove from the dryer immediately.
Let the curtain hang on the rod overnight. Sometimes the weight of the curtains is enough to pull out the wrinkles from polyester.
Turn a blow dryer on high heat and aim the dryer at the wrinkled area of the curtain. As the fabric heats, smooth out the wrinkles with your hands. Do not hold the dryer too close to the curtain, or direct the heat in one spot for more than a few seconds at a time, as some types of polyester could melt.
Steam out the wrinkles with a hand-held steamer. Hold the steam nozzle over the wrinkled area. With your free hand, tug gently on the fabric to straighten and smooth it. Work slowly, working from the top of the curtain down toward the floor.