A process and an apparatus for high-intensity drying of fiber webs or sheets, such as newsprint, printing and writing papers, packaging paper, and paperboard or linerboard, as they are formed on a paper machine. The invention uses direct contact between the wet fiber web or sheet and various molten heat transfer fluids, such as liquified eutectic metal alloys, to impart heat at high rates over prolonged durations, in order to achieve ambient boiling of moisture contained within the web. The molten fluid contact process causes steam vapor to emanate from the web surface, without dilution by ambient air; and it is differentiated from the evaporative drying techniques of the prior industrial art, which depend on the uses of steam-heated cylinders to supply heat to the paper web surface, and ambient air to carry away moisture, which is evaporated from the web surface. Contact between the wet fiber web and the molten fluid can be accomplished either by submersing the web within a molten bath or by coating the surface of the web with the molten media. Because of the high interfacial surface tension between the molten media and the cellulose fiber comprising the paper web, the molten media does not appreciately stick to the paper after it is dried. Steam generated from the paper web is collected and condensed without dilution by ambient air to allow heat recovery at significantly higher temperature levels than attainable in evaporative dryers.