Locate a flat surface in a warm and well-ventilated area that is out of direct sunlight. Temperatures above 70 degrees Fahrenheit are sufficient for speedy drying. Cover the surface with a thick towel.
Place the damp HEPA filter on the towel-covered surface. Wait for two hours.
Flip the cabinet HEPA filter over and place it in a new dry spot on the towel. Wait another hour.
Press gently on the HEPA filter to see if it has dried completely. Flip the filter to a new spot on the towel again, if it is still holding moisture. Reinstall the dry HEPA filter in the cabinet.