A constrained layer damper having a multilayer damping material is provided, as are related methods for making and using the damper. The constrained layer damper features a constraining layer, a carrier layer, a release liner, a viscoelastic layer interposed between the constraining layer and a first surface of the carrier layer, and a silicone pressure-sensitive adhesive interposed between the release liner and a second surface of the carrier layer. The silicone pressure-sensitive adhesive has sufficient tackiness at room temperature to adhere the constrained layer damper, with the release liner removed, to a substrate, such as a metallic substrate. The constrained layer damper has a peak damping temperature value in a range of about 50.degree. C. to about 100.degree. C.