Theoretical analysis and experimental study have been carried out on the thermal conduction during the discharge process in pulsed magnets. The simulation results show that, for the short pulse magnet, the results obtained from models with and without thermal conduction agree well with each other. The results from theoretical analysis and experiments are also in good agreement. For the long pulse magnet, the temperature difference between models with and without thermal conduction becomes non-negligible. The theoretical analysis shows that, for both short and long pulse magnets, the thermal conduction influences only the temperature distribution, not the waveform of the pulse magnetic field.