Copper busbar technology is widely used with the aim to achieve electrical connections with power distribution systems because of their flexibility and compactness. The thermal analysis takes into account the heat conduction and convection of a copper busbar system used to supply a test bench with high currents in order to check the electro-thermal behaviour of power circuit breakers during overload and short circuit conditions. This paper proposes a mathematical model for busbars used within a high current power supply. The obtained thermal model can be used to analyse the thermal behaviour of busbars in steady-state conditions at different values of the electric current, cross-section and length of the busbar. Also, the mathematical model allows to calculate the temperature distribution along the busbar at different values of the contact resistances at junction points with other conductors. There is a good correlation between calculated, simulated and experimental results.