A flexible, adhesively attachable, thermal and acoustical insulating shield has a needled, flexible, fibrous batt (40) having an insulating layer (43) of insulating fibers (44) disposed between opposite binding layers (41, 42) of binding fibers (45). Binding fibers (45) of each binding layer (41, 42) are needledly disposed through the insulating layer (43) and an opposite binding layer (41, 42) to provide tufts (46) of binding fibers (45) protruding from the opposite binding layer (41, 42) so as to form a tufted upper surface (47) and a tufted lower surface (48) of the batt (40). A flexible adhesive (50) is disposed and adhered substantially over the upper surface (47) and lower surface (48) of the batt (40) such that the tufts (46) on the upper and lower surfaces (47, 48) are secured to the surfaces by the adhesive. A flexible, protective foil (51) is permanently adhered by the adhesive (50) to the lower surface (48) of the batt. The shield may be flexed and pressed to configure and permanently attach the upper surface (47) to an object (1) to be shielded.