A system comprising: a manifold configured to be disposed adjacent to a tissue site; a patient-interface member comprising a first thermally-conductive, vapor-permeable material, the patient-interface member configured to be disposed adjacent a tissue site; a drape-interface member coupled to the patient-interface member and comprising a second thermally-conductive, vapor-permeable material; a liquid-processing member disposed between the patient-interface member and the drape-interface member, the liquid-processing member configured to temporarily store liquid; and a drape configured to be disposed over the patient-interface member and the drape-interface member, a surface of the drape further configured to contact and be fluidly coupled to a surface of the drape-interface member opposite the liquid-processing member; a reduced-pressure source fluidly coupled to the manifold; whereby the patient-interface member is configured to conduct thermal energy from the tissue site, the drape-interface member is configured to receive the thermal energy from the tissue site, and the conducted thermal energy is configured to increase the moisture vapor transmission rate of liquid from the liquid-processing member through the drape compared to the moisture transmission rate in the absence of the conduct thermal energy; wherein the patient-interface member and the drape-interface member comprise one or more of: an active carbon material, metallic fiber, zinc oxide, and silver; wherein the liquid-processing member comprises at least one of: a foam, a non-woven, a super absorbent material, and a gel material. a manifold configured to be disposed adjacent to a tissue site; a patient-interface member comprising a first thermally-conductive, vapor-permeable material, the patient-interface member configured to be disposed adjacent a tissue site; a drape-interface member coupled to the patient-interface member and comprising a second thermally-conductive, vapor-permeable material; a liquid-processing member disposed between the patient-interface member and the drape-interface member, the liquid-processing member configured to temporarily store liquid; and a drape configured to be disposed over the patient-interface member and the drape-interface member, a surface of the drape further configured to contact and be fluidly coupled to a surface of the drape-interface member opposite the liquid-processing member; a reduced-pressure source fluidly coupled to the manifold; whereby the patient-interface member is configured to conduct thermal energy from the tissue site, the drape-interface member is configured to receive the thermal energy from the tissue site, and the conducted thermal energy is configured to increase the moisture vapor transmission rate of liquid from the liquid-processing member through the drape compared to the moisture transmission rate in the absence of the conduct thermal energy; wherein the patient-interface member and the drape-interface member comprise one or more of: an active carbon material, metallic fiber, zinc oxide, and silver; wherein the liquid-processing member comprises at least one of: a foam, a non-woven, a super absorbent material, and a gel material.