This paper presents a laboratory method to measure the thermal properties of a carbon-carbon composite material that is characterized by an orthotropic thermal conductivity and isotropic volumetric heat capacity. Thermal properties are estimated using parameter estimation techniques with measured surface heat flux and temperature histories for an experiment with two-dimensional heat flow. Thermal properties were determined for a temperature range of 65-400 degrees C. The thermal conductivity parallel to the fibers is 12-15 times larger than the conductivity normal to the fiber. The results show excellent agreement with separate one-dimensional results, demonstrating a presumed quadratic relationship with temperature.