Two different methods are considered for the determination of the thermal conductivity of small particles (50-300 mu m) of char. Both methods are based on imposing a temperature gradient on a suspended particle. In the first, the thermal conductivity is obtained from measuring the photophoretic force induced by laser radiation on a suspended particle. Three patterns of behavior of the thermal conductivity during burning were observed: (a) a significant decrease of the thermal conductivity at low conversions, (b) a moderate change at intermediate conversions, and (c) a rise at high conversions. The observed changes of thermal conductivity are used to gain insights into the evolution of the porous structure during oxidation. The second method is based on a comparison of the shrinkage under oxidation in regime I of evenly heated particles with those that are unevenly heated. The method also supports previous models and observations of shrinkage of highly porous chars in regime I. The two methods agree well for the thermal conductivity of highly porous chars.