The power flow limits of transmission lines are set in order to ensure a given level of security to the electric system; their improper definition can reduce system reliability, increase the curtailment of renewable energy sources or create barriers to the free trading of energy. Unlike the previous literature, the Dynamic Thermal Rating procedure here proposed takes into account not only that the temperature of conductors can vary span by span for different weather conditions, but also the mechanical interaction between spans, due to their different elongation and to the consequent rotation of insulator strings. The developed tool is able to forecast the time trend of conductor temperatures, tensions, sags and clearances at each span, or to indicate which current can be carried for a given time before a clearance or temperature constraint is violated. Several case studies compares the results of this novel method with the outcomes of the traditional "ruling span" technique, especially when using High-Temperature Low-Sag (HTLS) conductors, having non-linear behaviour with respect to temperature.