The thermal diffusivities Dth of mullite single crystals with about 2/1-composition parallel to the crystallographic a, b, and c axes (i.e., parallel to , , and ) and of monophase, dense mullite ceramics were measured between room temperature and 1200°C using the laser flash method. The semi-transparent mullite disks were covered by thin layers of argon-sputtered platinum and sprayed colloidal graphite in order to minimize heat radiation transfer effects. The phonon-produced thermal conductivity of mullite was calculated according to K=DthCp using experimentally measured values for thermal diffusivity, Dth(T), and specific heat, Cp(T), and thermal expansion coefficients, αi, for the determination of temperature-dependent density (T) and sample thickness d(T). The anisotropy of thermal diffusivity and conductivity is evident with highest values parallel to the crystallographic c axis (i.e., ; e.g., at T=100°C K=6.862 W/mK), corresponding to the direction of strongest bonds and highest elastic stiffness in the mullite crystal structure. Perpendicular to the c axis, thermal diffusivities and conductivities are smaller, with the values parallel to the a axis (i.e., ) being slightly higher than parallel to b (i.e., ; e.g., at T=100°C K=4.563 W/mK and K=4.400 W/mK), indicating lower bond strength and elastic stiffness in these crystallographic directions. Conductivity anisotropy factors are around 1.33 for K/Kaverage, 0.90 for K/Kaverage, and 0.85 for K/Kaverage with little variation between room temperature and 1200°C. The thermal diffusivity and conductivity of dense, monophase mullite ceramics display similar values as the averaged single crystal data, thus providing a master curve for the temperature-dependent thermal conductivity.