In this work a complete coupled electrothrmal analysis of overhead power lines is presented. The electromagnetic field problem is soved analytically for both the AAC and ACSR cases. The Joule losses thus computed are input to the thermal problem yielding the analytical expression of the thermal impedance. A subsequent novel dynamic thermal analysis of the almost periodic load variations during an extended time period allows the prediction of temperature fluctuations (value and delay) and the prevention of the line expansion and/or overheating.