A novel approach to determine absolute values of thermal conductivity of single micron-sized particles, has been developed. A particle was suspended in an electrodynamic chamber and was unevenly irradiated to impose a temperature gradient within the particle, by a focused CO2 laser beam. Consequently, a photophoretic force was generated from which the particle thermal conductivity was determined. Maximum uncertainty was estimated to be about 25%. Thermal conductivity of highly porous char particles was measured as a function temperature, in the range of 350-1150 K, showing increase of thermal conductivity with temperature.