An apparatus and process for forming heat-transfer elements wherein platelike fins are secured to the outside wall of a heat-transfer tube. There is provided a bullet-shaped tool which is axially slidably inserted into the heat-transfer tube to effect radial expansion thereof into gripping engagement with the surrounding fins. The tool is freely rotatably supported on the end of a pushing rod, and the peripheral surface of the tool has spiral grooves therein which define small teeth therebetween. By axially pushing the tool into the tube, the teeth bite into the internal wall of the tube and, due to the helical orientation of these teeth, the axial displacement of the tool into the tube causes the tool to simultaneously rotate. This causes not only radial expansion of the tube for gripping the fins, but simultaneously results in the formation of spiral-like grooves on the internal wall of the tube.