A heat energy transfer device has an enclosure defining a closed cavity and including an outer face to be heated or cooled. A heat transfer medium is contained in the cavity. The device has a first capillary arrangement disposed in the cavity for advancing the heat transfer medium in the liquid phase in a first direction parallel to the outer face of the enclosure and a second capillary arrangement disposed in the cavity for advancing the heat transfer medium in the liquid phase in a second direction parallel to the outer face of the enclosure. The first and second directions are non-parallel to one another.