The invention concerns an apparatus wherein each pair of jaws (42) is mounted on a carriage (29, 31) freely mobile on longitudinal slide rails and subjected to the action of springs (28, 32) pushing them towards a retractable stop borne by the frame of the other carriage, while the frame (1) of one of the carriages (29) is itself mounted sliding on transverse slide rails (8) and is coupled to drive means (10) capable of moving it on said rails (8) between an initial position, wherein the pairs of jaws (42, 43) are aligned, and a connecting position, wherein the pairs of jaws are offset and the retractable stops retracted, and the hot blade is borne by a carriage vertically mobile, in both directions, on vertical slide rails (20), said carriage (27) having the shape of a wedge whereof the two lateral sides are profiled and co-operate each, after the retractable stops are retracted and while the blade (27) is being raised, with a roller having a horizontal axis projecting rearward of the corresponding frame or jaw-bearing carriage, to control the travel and the abutting efforts of the tube to be connected.