The present invention concerns a machine (10) for covering paper articles (1) with a sheet (2) of flexible thermoplastic material, comprising: ·cutting means (110), comprising a bar (110') provided with a heatable cutting tool (112) able to assume an operating position, in contact with the sheet (2), and a non-operating position, outside contact with the sheet (2); ·control means (120), able to determine the operating position of the cutting tool (112) for heat sealing and/or cutting the sheet (2). The machine (10) furthermore comprises means for controlling the temperature of the cutting tool, operatively connected with the control means (120) to determine the operating position when a pre-defined temperature threshold is reached by the cutting tool.