A self-wrapping, textile sleeve for routing and protecting elongate members from exposure to abrasion, thermal and other environmental conditions and method on construction thereof. The sleeve has an elongate wall constructed from interlaced yarns having interstices between adjacent yarns. At least one of the yarns is heat formed at one temperature to form the wall as a self-wrapping wall curling about a longitudinal axis of the sleeve. The wall has an inner surface providing a generally tubular cavity in which the elongate members are received. The wall also has an outer surface with a cured layer thereon. The cured layer is cured at the one temperature at which the yarns are heat formed into their self-wrapping configuration, wherein the cured layer fills the interstices between adjunct yarns to form an impervious layer on the wall.