a thermoplastic board comprising at least one smooth side edge is produced by means of extrusion . the side edge of a synthetic web is heated at least to its melting temperature following calibration while the peripheral surface zones are kept at a temperature below the softening temperature by cooling . a smoothing device for a side edge of the thermoplastic board encompasses a guiding groove that is provided with at least one heating means , located within the face , and at least one respective cooling means located within the side surfaces that face each other . a cutting edge of a synthetic board that can be guided inside the guiding groove rests against the face while the peripheral surface zones thereof lean against the side surfaces .