A pipe network for conveying a fluid, designed to be submerged in an expanse of water, comprising: - an intermediate coupling for connecting rigid pipe elements (24, 26, 28) for conveying a fluid, designed to be submerged in an expanse of water, comprising: • an inner rigid shell, comprising: * an inner section, the inner section delimiting an inner passage for a flow of fluid between a first end and a second end, * at least one inner branch tapped on the inner section between the first end and the second end, the inner branch delimiting an inner aperture for a fluid flow emerging in the inner passage; • at least one electric connecting line (68A, 68B) positioned outside the inner shell, the electric line (68A, 68B) having a first electrical connecting point situated on a first side of the inner branch, and a second electrical connecting point situated on a second side of the inner branch, the coupling comprising a rigid outer shell positioned around the inner shell, the outer shell at least partially covering the inner section on either side of the inner branch, and the inner branch, the outer shell and the inner shell delimiting an intermediate space between them extending around the inner section and the inner branch, the electric line (68A, 68B) being received in the intermediate space, the coupling comprising a thermally insulating layer positioned in the intermediate space across from the inner section and across from the inner branch; - a first rigid pipe element for conveying a fluid, coupled to the first end of the inner section; - a second rigid pipe element for conveying a fluid, coupled to the second end of the inner section; - a third rigid pipe element for conveying a fluid coupled to the inner branch; the first rigid pipe element and the second rigid pipe element each comprising an inner fluid guide tube coupled to the inner section and an outer tube delimiting an annular space with the inner tube, the annular space receiving a thermally insulating layer and at least one electric line designed to heat the fluid contained in the inner tube, the electric lines of the first rigid pipe element and the second rigid pipe element being electrically coupled to each other by the electric connecting line (68A, 68B), characterized in that the electric line (68A, 68B) is intended to heat the fluid flowing in the inner shell of the intermediate coupling, the electric line (68A, 68B) being placed in thermal contact with the inner shell to heat the fluid contained in the inner passage. - an intermediate coupling for connecting rigid pipe elements (24, 26, 28) for conveying a fluid, designed to be submerged in an expanse of water, comprising: • an inner rigid shell, comprising: * an inner section, the inner section delimiting an inner passage for a flow of fluid between a first end and a second end, * at least one inner branch tapped on the inner section between the first end and the second end, the inner branch delimiting an inner aperture for a fluid flow emerging in the inner passage; • at least one electric connecting line (68A, 68B) positioned outside the inner shell, the electric line (68A, 68B) having a first electrical connecting point situated on a first side of the inner branch, and a second electrical connecting point situated on a second side of the inner branch, the coupling comprising a rigid outer shell positioned around the inner shell, the outer shell at least partially covering the inner section on either side of the inner branch, and the inner branch, the outer shell and the inner shell delimiting an intermediate space between them extending around the inner section and the inner branch, the electric line (68A, 68B) being received in the intermediate space, the coupling comprising a thermally insulating layer positioned in the intermediate space across from the inner section and across from the inner branch; • an inner rigid shell, comprising: * an inner section, the inner section delimiting an inner passage for a flow of fluid between a first end and a second end, * at least one inner branch tapped on the inner section between the first end and the second end, the inner branch delimiting an inner aperture for a fluid flow emerging in the inner passage; * an inner section, the inner section delimiting an inner passage for a flow of fluid between a first end and a second end, * at least one inner branch tapped on the inner section between the first end and the second end, the inner branch delimiting an inner aperture for a fluid flow emerging in the inner passage; • at least one electric connecting line (68A, 68B) positioned outside the inner shell, the electric line (68A, 68B) having a first electrical connecting point situated on a first side of the inner branch, and a second electrical connecting point situated on a second side of the inner branch, the coupling comprising a rigid outer shell positioned around the inner shell, the outer shell at least partially covering the inner section on either side of the inner branch, and the inner branch, the outer shell and the inner shell delimiting an intermediate space between them extending around the inner section and the inner branch, the electric line (68A, 68B) being received in the intermediate space, the coupling comprising a thermally insulating layer positioned in the intermediate space across from the inner section and across from the inner branch; - a first rigid pipe element for conveying a fluid, coupled to the first end of the inner section; - a second rigid pipe element for conveying a fluid, coupled to the second end of the inner section; - a third rigid pipe element for conveying a fluid coupled to the inner branch;