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A precise and efficient finite element model has been developed to solve the coupling of the magnetic field and heating in pulsed coils energized by a capacitor bank. The magnetic field and the current density distribution in each conductor layer of the coil are simulated, taking into account the eddy current, magneto-resistance and heat conduction. The temperature distribution in the conductor during the discharge is also calculated. Eddy currents and magneto-resistance result in a large temperature gradient across the layers. The calculated pulsed field waveform is in good agreement with experimental results for a large range of pulsed coils; this provides useful insight for optimized coil design.