An apparatus for shaping a glass sheet includes an engagement member including a flexible bumper comprising a flexible material. The flexible bumper is configured to operate at the forming temperature to reduce an impact stress between the engagement member and the edge portion of the glass sheet. In another example, an apparatus for shaping a sheet of glass includes a push member configured to engage an end edge portion of the glass sheet to push the glass sheet to be transported over the support surface. The push member includes a push flange extending in a direction away from the support surface. The push flange includes a plurality of apertures configured to increase the resistance of conductive heat transfer between the end edge portion of the glass sheet and the push member. In a further example an engagement member can fabricated from a material having a coefficient of thermal conductivity that is less than a coefficient of thermal conductivity of the stainless steel. In further examples, methods include using the apparatus to shape a glass sheet.