The thermal conductivity of the composite cathode, which consists of polymer electrolyte and active material, is an important parameter for the thermal management and heat transport studies of lithium polymer batteries. Thermal conductivities of TiS2 and V6O13 composite cathode were measured by a guarded hear flowmeter over the lithium polymer batteries operating temperature range from 25 to 150 degrees C. They were found to increase with the temperature up to the melting temperature of the polymer electrolyte, but to increase only slightly after the melting temperature. A heat transport mechanism of phonon transmission in the polymer electrolyte matrix and transport of lithium ions in the active materials can be used to explain the results. The effective thermal conductivity of the composite cathode can be estimated from the conductivities of polymer electrolyte and active materials. To determine the latter, measurements were also made of the thermal conductivities of Dressed samples of TiS2 and V6O13 The measurements of composite cathodes, along with measurements of lithium polymer electrolytes, previously published by this journal, complete the work on the thermal conductivities of lithium polymer battery cell components, which can be used to estimate the thermal conductivities of the cell using thermal-resistance-in-series/parallel models.