A protective braided sleeve and method of construction thereof is provided. The sleeve includes a seamless, circumferentially continuous, tubular braided wall having a cavity extending lengthwise along a central longitudinal axis between opposite ends. The wall includes a plurality of yarns braided with one another, with at least one or more of the yarns including a bicomponent yarn including a core and an outer adhesive sheath adapted to be selectively melted to bond the wall to an elongate member extending through the cavity.