Method for evaluating temperatures in active heave compensation ropes characterized by comprising the following steps: - describe the geometry of ropes as composite structures obtained through assemblies of helical components in hierarchical levels: wires, strands and the rope itself, the parameters describing the geometry of a rope being the helix radius, the pitch and the swept angle of a wire in a strand (Rw, Pw, θw) and of a strand in a rope (Rs, Ps, θs); - starting from the parameters describing the geometry of a wire in a strand (Rw, Pw, θw), use a mechanical model of the strand that represents the material properties of each wire, under the assumption of linear elastic behavior, by specifying the Young modulus (E) and the Poisson coefficient (v), the parameters describing the mechanical behaviour of the strand being the axial force (F s ), the torsional moment (M s1 ) and the bending moment (M s2 ); - starting from the parameters describing the geometry of a strand in a rope (Rs, Ps, θs), use a mechanical model of the rope that represents the combined action of tensile loads and imposed bending curvature, the parameters describing the mechanical behaviour of the rope being the tensile load (Fr) and the bending moment (M r ); - based on the fact that whenever a strand or a wire rope is cyclically bent over a sheave, a portion of the total mechanical power provided as input to the system is dissipated through frictional phenomena which are a function of the parameters describing the mechanical behaviour of the strand and of the rope, use a thermal model for the evaluation of the rope temperature increase (Ts) with respect to the ambient temperature, the thermal model comprising two main dissipation sources: the friction between strands or rope and a sheave and the friction between wires or between strands; - compare the rope temperature increase (Ts) obtained by the thermal model with a value of a predetermined temperature threshold. - describe the geometry of ropes as composite structures obtained through assemblies of helical components in hierarchical levels: wires, strands and the rope itself, the parameters describing the geometry of a rope being the helix radius, the pitch and the swept angle of a wire in a strand (Rw, Pw, θw) and of a strand in a rope (Rs, Ps, θs); - starting from the parameters describing the geometry of a wire in a strand (Rw, Pw, θw), use a mechanical model of the strand that represents the material properties of each wire, under the assumption of linear elastic behavior, by specifying the Young modulus (E) and the Poisson coefficient (v), the parameters describing the mechanical behaviour of the strand being the axial force (F s ), the torsional moment (M s1 ) and the bending moment (M s2 ); - starting from the parameters describing the geometry of a strand in a rope (Rs, Ps, θs), use a mechanical model of the rope that represents the combined action of tensile loads and imposed bending curvature, the parameters describing the mechanical behaviour of the rope being the tensile load (Fr) and the bending moment (M r ); - based on the fact that whenever a strand or a wire rope is cyclically bent over a sheave, a portion of the total mechanical power provided as input to the system is dissipated through frictional phenomena which are a function of the parameters describing the mechanical behaviour of the strand and of the rope, use a thermal model for the evaluation of the rope temperature increase (Ts) with respect to the ambient temperature, the thermal model comprising two main dissipation sources: the friction between strands or rope and a sheave and the friction between wires or between strands; - compare the rope temperature increase (Ts) obtained by the thermal model with a value of a predetermined temperature threshold. <EOS>