A union connection between uncooled pipe and cooled double-wall pipe in a heat exchanger comprising a double-wall pipe comprising in turn an internal pipe traveled by a fluid to be cooled and an external pipe defining with the internal pipe an air space traveled by a cooling fluid with one end of the double-wall pipe being connected to an inlet duct of the fluid to be cooled through a connection part also forming a bottom wall of the air space virtually transversal to the double-wall pipe extension and characterized in that the connection part has an annular form with U cross section to define two annular shanks extending longitudinally to the pipe with each shank being welded to one end of one of the two pipes of the double-wall pipe and in that the end of the inlet duct is welded to the connection part at said bottom wall of the air space.