In this paper, we present a new numerical model, in which both the thermal and the electromagnetic aspects of the over-critical current regime of HTS materials are taken into account. The electromagnetic and thermal equations have been implemented in finite-element-method (FEM) software in order to obtain a novel, closer to reality model for investigating the behaviour of the superconductor when the current exceeds $I_{c}$. This model has been applied for studying the behaviour of strip lines of an YBCO/Au FCL with a sapphire substrate. Simulations with currents largely exceeding $I_{c}$ have been performed, showing that the total current limitation occurs only when the temperature dependence of the electrical parameters is taken into consideration. Such modelling can replace experiments with currents far exceeding $I_{c}$ which may damage or destroy the studied sample or HTS device.