Low- and medium-voltage connectors are designed for a service life of more than 30 years, during which they have to withstand extreme conditions, so it is primordial ensuring their thermal performance. Mandatory standardised short-circuit tests are required to homologate electrical connectors which are conducted in singular and scarce laboratories, so it is essential to dispose of fast and accurate simulation tools to predict the thermal performance of the equipment during the design stage. This study focuses on the application of a fast and accurate simulation method to reproduce the transient thermal behaviour and to estimate the transient temperature rise and the subsequent cooling of power connectors during short circuits. To minimise the computational burden, this study proposes a fast finite-difference method approach, based on one-dimensional reduction of the analysed geometry. To improve accuracy, key three-dimensional information is retained, such as the convective coefficients, the incremental resistance or the cross-section of each node. Results attained by means of the proposed method are validated against experimental results conducted in a high-current laboratory, thus corroborating the usefulness and accuracy of the proposed method. The methodology exposed in this study can be applied to many other hardware for power lines and substations.