Abstract: An electromagnet coil comprising Litz wire windings and power leads without break or interruption is cooled by a perfluorinated liquid by sensible and phase change heat transfer in a closed system. The electromagnet coil may be housed in a pentagonal or hexagonal pressure vessel to allow high packing densities in an array or helmet configuration. The helmet is then lowered over a human cranium for transcranial electromagnetic stimulation. The Litz wire windings reduce the power and voltages required for operation, yet allow production of over 2 T of accurately directed magnetic pulses for direct nerve or neuron stimulation. The perfluorinated liquid maintains the temperature of the helmet to less than 35-40° C., ensuring a comfortable temperature device for a human test subject. A utility cable connects the helmet to an external cooling unit and an external power supply.