The thermal conductivity of STYCAST reinforced Bi(2223) superconducting materials has been studied between 10 and 150K using a steady-state heat flow method. The value of heat leakage per pair of bulk leads from 4.2K to 77.3K for the composite materials has been estimated from the thermal conductivity data. The measured thermal conductivity of the composite materials below 100K is in rough agreement with the value obtained from the mixtures rule of Bi(2223) and STYCAST. It is found that the heat intrusion of the reinforced materials is one-fourth as small as that of 800 A-class conventional gas-cooled current leads. The thermal conductivity of Bi(2223) superconducting material has been studied from 30K to 130K in constant magnetic fields up to 13T. The thermal conductivity value of the Bi(2223) material is strongly suppressed as the applied field is increased along the c-axis of the sample. The contribution of the magnetic field to the value of heat leakage for the current leads of the high-T_c materials is negligible even in high fields. Therefore, STYCAST reinforced Bi(2223) superconducting materials are suitable for current leads to design the high-field and/or large-scale superconducting magnet with a cryocooler-cooled type using no liquid helium.