Increases in the proportion of variable renewable energy sources (var-RES) in electrical power networks are accompanied by increased fluctuations in the conductor currents and an increased risk of conductors exceeding their thermal ratings. Dynamic line ratings, which use real-time loading and weather information to continuously adjust the thermal ratings of conductors, are one of the measures that has been applied to increase the loadability while addressing the challenges caused by increased current fluctuations. However, the mathematical models that have been developed based on the empirically observed conductor thermal dynamics show that the relationships between the conductor temperature and both the current and ambient weather conditions are nonlinear. This makes it difficult to incorporate the conductor electro-thermal characteristics when specifying the line ratings. This paper presents numerical approximations of the various components used in the International Council on Large Electric Systems (CIGRE) physical model in order to simplify estimations of the temperature of overhead conductors under dynamic line ratings regimes. The resulting simple equations can be used to directly estimate the conductor temperature without the need for iterative calculations, which are required in the full CIGRE model. Comparisons between the simplified model and the full CIGRE model are provided for validation purposes.