A wrappable textile sleeve and method of construction thereof is provided. The sleeve has a wall of interlaced yarn with opposite edges extending lengthwise between opposite ends. The opposite edges of the wall are wrappable to overlap one another to form a tubular cavity. At least one electro-functional member extends lengthwise between the opposite ends of the wall. The at least one electro-functional member is interlaced in the wall at a plurality of nodes and forms at least one unrestrained loop intermediate the opposite ends of the sleeve. The at least one electro-functional member has a straightened length that is greater than the straightened length of the sleeve, thereby allowing opposite ends of the at least one electro-functional member to be pulled axially outwardly away from the ends of the sleeve to form leads for attachment to a power source, which in turn constricts the at least one loop.