The standard calculation methods of IEEE, CIGRE, and IEC working groups are widely employed by the industry to determine current-carrying capability of bare overhead (OHL) conductors. However, these methods include several simplifications within the heat transfer mechanisms between the conductor and its surroundings. At present, they are different particularly at low wind conditions and are not well formulated for the use on High-Temperature Low-Sag (HTLS) conductors at Ã¢ÂÂhighÃ¢ÂÂ temperatures. Therefore, the source of these simplifications are discussed in the first part of the thesis in a comparative study of considering the fundamental physical concepts of the involved heat transfer mechanisms. This project is aimed at enhancing the appropriateness of the existing calculation methods and subsequently developing a unified current-temperature calculation approach for OHL conductors. For this, the impact of mixed convective cooling mechanism, conductor structural design (e.g. aerodynamic), and bundle configurations which are simplified within the standard methods are studied during the low wind and Ã¢ÂÂhighÃ¢ÂÂ operating temperatures. The Finite Element Modelling (FEM) of COMSOL Multi-physics software package, acknowledged as an appropriate tool to capture these simplified elements is used to perform various heat transfer phenomena analyses on both conventional and HTLS conductors. Based on these results, new equations that advance the existing standard methods to calculate convective cooling mechanism PC, radiative cooling mechanism PR, and radial temperature gradient Tc-Ts of overhead line (OHL) conductors are subsequently formulated. These proposed methods could be utilised for round and trapezoidal conductors that operate at less than 1 m/s and temperatures up to 250 ÃÂ°C. The thesis also discusses possible thermal benefits from applying grease on conductors and provides recommendations to advance the existing current-temperature calculation practices of bundled conductors. The main outcome of this evaluation highlights the importance of using high accuracy calculation approach that captures the wire shapes, the combined effect of natural and forced convection mechanisms, and position of conductor with respect to wind in bundle configuration particularly at low wind and Ã¢ÂÂhighÃ¢ÂÂ operating temperatures as presented by the formulated equations within the thesis. Due to these improvements, the errors of the standard methods for single conductors that usually ranging from 2% - 6% within the low-wind and medium-wind zones are reduced by at least 50%. These findings are valuable for designing OHL power networks operational limit especially when actual weather conditions are available in order to maximise their security clearance and power transfer capability.