This paper is focused on simulations of how a superconductor reacts to extreme, suddenly changing operation conditions imposed by strong over-currents. An attempt is made to shed light on the physics of current transport behind, as far as this can be achieved with numerical simulations. For this purpose, temperature and current distribution in multi-filamentary high-temperature superconductors is investigated in a finite element analysis with high spatial and time resolution. An extra subsection is devoted to the involved heat transfer problem. As a result, resistive (Ohmic and flux flow) and zero loss states would co-exist in parallel if over-current cannot be compensated, for example, by switching it to a shunt. Anisotropic thermal diffusivity of high-temperature superconductors, in particular of BSCCO, would obstruct thermalisation of losses, and compensating of field and current in-homogeneities would become impossible within acceptable periods of time.