Transmission lines have a fundamental role in the electric system performance,connecting power sources to load centers. When the transmission system attains it`s transmission capability limit, the system must be expanded, either constructing new lines, or upgrading existing ones. Among the factors that can limit a transmission line transfer capability is the operating temperature limit, established for both economic and safety reasons. Due to its geographic extension the construction of a transmission line involves a big economic as well as environmental cost. For this reasons the upgrade of existing lines, in the sense of increasing it`s transmission capability, has become a priority to electric utilities and a main option for system expansion. In this work the problem of transmission line conductors` operational temperature is analised and the methodology presently used to establish it`s operational limit is described. Two models to forecast transmission line conductors` temperature are developped:a complete model which uses forecasts of the relevant metheorological variables,and a direct model using univariate methods on temperature series. In the development of forecasting models, linear stochastic methods such as exponential smoothing and Box-Jenkins, as well as Artificial Neural Networks techniques were used.Finally model validation is presented, showing very good performance of the proposed forecasting models, and some potential applications are suggested.