The present invention discloses a planishing method for joined sheets made of a thermoplastic material. Welded ends (38) of the plastic sheets (28,30) are placed between two platens (22,24). The platens are heated to raise the temperature of the plastic material a sufficient amount to soften the plastic material without disturbing its molecular structure. The platens are pressed together with a sufficient pressure while applying heat until the sheets are pressed together providing a relatively smooth, continuous joint having a thickness similar to the thickness of a single sheet. Finally, the platens are cooled thereby cooling the joined sheets.