We examined the possibility of the practical use of a conduction cooled magnetic shield type fault current limiter from the view point of a thermal design. The thermal calculation was carried out with a small model using the Nb3Sn wire with low sc loss, Pie found that the temperature increase of the small model was insignificant. We also confirmed the current limiting operation in an experiment, The conceptual design and the thermal calculation of the conduction cooled fault current limiter for a distribution pou er system is also discussed in this report.