An improved compactor shoe of the type having a gull-wing shape formed by a first wing and a second wing that meet at a critical lower edge, and a top surface. The first wing has a first radius of curvature and the second wing has a second radius of curvature, and both depend concavingly from the top surface to the critical lower edge. The first radius of curvature of the first wing is less than the second radius of curvature of the second wing. The improvement includes a through bore extending axially through the shoe, which carries a coolant to avoid heat deformation of the critical lower edge.