The purpose of this investigation was to develop an apparatus to measure the thermal conductivity of polymer melts, and to use the apparatus to measure the thermal conductivity of selected melts as a function of melt temperature. The steady-state, coaxial cylinder method with guard heaters was used and the annular gap was 0.075 inch. The polymer was melted in a cylindrical melt chamber, then metered to the thermal conductivity measuring apparatus. Cartridge heaters provided heat input and temperature measurements were made with calibrated, differential, iron-constantan thermocouples. The thermal conductivity of polyethylene, polystyrene and nylon melts tested increased with increased temperature. The thermal conductivity of the polypropylene sample was temperature independent. Complexity of molecular structure lowered melt thermal conductivity. Radiation losses were accounted for and convection was determined to be absent. The results were shown to be within a 3 percent experimental measurement error. Meaningful confidence limits cannot be calculated because of the limited number of data points. / Master of Science