Abstract: For all-over lining of a longitudinally slit pipe insulating shell consisting of mineral fibers, with a foil having a coating of a heat activatable adhesive, a fully automatic process uses the steps of bringing the foil into a preliminary position with its end portion bent over downwardly by means of a rail, subsequently moving the foil into a position of readiness in which its outer edge comes to bear on a vertically adjustable heating roller, so that an initial activation of the adhesive starts to take place, then raising the heating roller to the pipe insulating shell and permitting it to remain in this adhering position for a brief period, and finally carrying out the actual lining operation by rotating both the heating roller and the pipe insulating shell at the same peripheral speed, and in opposite direction by means of a winding mandrel.