Abstract: The apparatus for connecting objects by means of a plastically deformable connecting body comprises a shaping punch (4), a flow-restricting wall (5) closely surrounding the shaping punch and a gas supply lead (6) through which a gaseous medium can be introduced into the gap between the shaping punch (4) and the flow-restricting means (5). The shaping punch (4) has a heating cartridge (8) by means of which the lower end of the shaping punch can be heated. Provided on the outside of this shaping punch are heat-transfer ribs (9) which are used to heat up the supplied, gaseous medium which emerges at the lower end of the flow-restricting means in order to produce a flow around a plastically deformable connecting body (3), so that the latter is uniformly heated for the deforming process. The connecting body (3) is also integrally formed on a part (2) and reaches through a hole in a second part (1) which is to be connected to the first part.