Fill a sink with water and a mild detergent. Take the soap suds and place on the Tempur-Pedic foam.
Rub the suds into the mattress with a sponge or towel. Fill an empty spray bottle with water, and lightly spray the mattress. Soak up the water with a towel or sponge.
Sprinkle baking soda over the mattress, and let it sit for several minutes. Vacuum the mattress. The baking soda will help keep the mattress smelling fresh.
Dry the mattress with a hair dryer on a low setting until the mattress is dry to the touch. Use a fan to finish drying before putting sheets back on the mattress.