The reaction of an equilibrium tokamak plasma to a sudden localized deposition of heat is investigated by means of numerical simulations of the time-dependent equations of resistive magnetohydrodynamics (MHD) in two spatial dimensions, in order to obtain a better understanding of the structure and dynamics of the hot plasma filaments that are observed in recent tokamak experiments. Simulation results show that the fast heating generates MHD waves and creates a localised hot filament. Pressure perturbations are carried away from the heated area by slow waves, even when the heating is applied on the Alfvén time scale. When a temperature-dependent resistivity is considered, a current peak is formed at the place of the temperature peak, and the order of magnitude of the current is given by the condition that ηJz is constant. Next to the wave dynamics, the simulations show another type of hot filament dynamics caused by j×B forces. These forces drive filaments to the centre of the plasma at a nearly constant velocity, which decreases for smaller resistivities. Two filaments can merge under the influence of this current–current interaction. This process happens on a very long time scale. For realistic tokamak resistivities, the coalescence of filaments may take place on time scales of the order of the experimentally reported lifetime of filaments, and may thus be the mechanism that determines the lifetime of the filamentation process.