An assembly of two coaxial pipes of the PiP type, having at least two coaxial pipe unit elements each with an inner pipe and an outer pipe, defining an annular space, filled with an insulating material, and assembled end to end by welding, including a sleeve with a hollow tubular wall made of rigid or semirigid material, preferably of plastics material or composite material, surrounding the pipe in register with the welded junction zone between the two coaxial pipe unit elements, the hollow tubular wall of the sleeve having an outer casing and an inner casing connected together at their longitudinal ends in leaktight manner, thereby defining an internal volume that is completely filled with a quasi-incompressible thermally insulating material.