A method of monitoring thermomechanical behavior of an undersea pipe (2) transporting fluid under pressure and made by assembling unit pipe elements (4), comprising determining a mechanical signature specific to each unit pipe element, using a measurement cable (16) having an optical fiber sensor using Brillouin backscattering to measure deformation of the pipe element while it is subjected on land to various mechanical stresses in predetermined directions and magnitudes, and establishing a stiffness matrix associated with the mechanical signature of each pipe element, a step of determining a thermal signature specific to each unit pipe element, which step consists in measuring the temperature changes of the unit pipe element while it is being subjected on land to various different electrical heating powers, and in establishing a thermal transfer function associated with the thermal signature of each pipe element, and a monitoring step consisting of recovering.