The major drawback for the commercialization of fault current limiter (FCL) made of YBCO on sapphire is their expensive price. In the recent years, coated conductors (CC) have been extensively developed and, due to their lower prices, have been recently tested for current limitation application. One weakness of these CC is the very low electric fields they can sustain, typically below 1 V/cm as compared to 20-40 V/cm observed in YBCO films grown on sapphire. The limitation of this electric field in CC comes certainly from the very low propagation velocities of the dissipative state, a property which might be correlated with the poor thermal behavior of the architecture of these materials. Both the thermal conductivities of the Hastelloy substrate and of the conducting bilayer (superconducting DyBCO and Ag conducting layer) influence the thermal behavior of the CC and therefore have to be optimized to get the best performance. We have then investigated the thermal and electrical behavior and the propagation velocities in CC during constant current pulses above. The comparison with the results obtained on YBCO films grown on sapphire shows several differences. In CC, the flux flow resistivities are 2-3 orders of magnitude higher than in film grown on sapphire and quench propagation velocities are 2-3 orders of magnitude lower (of the order of cm/s). The propagation velocities in CC and in films on sapphire are analysed with a simple adiabatic model.