A relationship between a temperature T 1 of a power line or power transmission conductor 10, an electrical quantity of the power line such as a current I or power flow P through the power line, as well as meteorological quantities or ambient conditions of the power line such as wind speed W , wind direction, humidity, solar radiation S and ambient temperature T a , is established in the form of a thermal model of the power line. Values of the aforementioned quantities or variables are continuously measured, and the collected values of the quantities are evaluated in order to update model parameters of the thermal model during operation of the power line. In a preferred embodiment of the invention, an average temperature representative of the entire line is determined via two Phasor Measurement Units (PMU) 11, 11' providing synchronized phasor values from two ends of the power line. An ohmic resistance of the power line is computed from the phasor values, from which in turn the average line temperature can be derived.