An osmotic transport apparatus includes a heat conducting chamber having an inner wall, a heat absorption end and a heat dissipation end, an osmotic membrane extending substantially longitudinally along an inner wall of the heat conducting chamber from the heat absorption end to the heat dissipation end, a liquid salt solution disposed in the osmotic membrane, and an inner vapor cavity so that when heat is applied to the heat absorption end, vapor is expelled from the osmotic membrane at the heat absorption end, is condensed on the osmotic membrane at the heat dissipation end, and is drawn into the osmotic membrane at the heat dissipation end for passive pumping transport back to the heat absorption end as more condensate is drawn through the osmotic membrane.