Multilayered web stock is directed toward a curved surface and at least one layer of the web stock is heated to a temperature above a glass transition temperature of the at least one layer of the web stock. The heating can occur just before or upon engaging the curved surface. The temperature of the at least one layer remains above the glass transition temperature while engaging the curved surface, allowing reshaping and/or realignment of the at least one layer relative to other layers of the web stock according to conformance to the curved surface. The web stock is cooled before it disengages from the curved surface. The heating can be done with a high power infrared lamp focused into a line across the web stock, and the cooling can be done with a cooled fluid jet. Additionally, a preheater can be employed, and a supplemental cooler can be used.