A media drying system removes a moistening liquid from a moistened medium. A liquid reservoir containing a heating liquid heated above a moistening-liquid boiling point. A rotatable liquid-blocking member has a liquid-blocking layer with an inner surface and an outer surface. A media-transport system transports the moistened medium so it contacts or is entrained around the liquid-blocking member in a path zone so that the moistened medium is brought into contact with the outer surface of the liquid-blocking layer. A porous material absorbs heating liquid from the liquid reservoir and brings the absorbed heating liquid into contact with the inner surface of the liquid-blocking layer for at least a portion of the path zone. Heat is transferred through the liquid-blocking layer from the absorbed warmed heating liquid to the moistening liquid, vaporizing the moistening liquid and removing it from the moistened medium.