A thermal sleeve for routing and protecting elongate members and method of construction thereof are provided. The sleeve has a tubular woven wall extending along a central axis between opposite open ends with an outer reflective foil layer fixed thereto. The wall is woven with lengthwise extending warp yarns and circumferentially extending fill yarns. The fill yarns include first and second fill yarns bundled in side-by-side abutting relation as a single pick, thereby forming discrete single pick bundles in axially spaced relation from one another. The first fill yarn is provided as a standard monofilament, while the second fill yarn is provided having a low melt material melted and bonded to the abutting first fill yarn and to portions of the abutting warp yarns, wherein the spaces between the discrete bundles remain substantially free of melted material, thereby further enhancing longitudinal flexibility of the sleeve.