The purposes of this study were to determine as a function of temperature the thermal diffusivity and/or thermal conductivity of SiC-Mullite and SiC-SiC, and to explain the observed behavior in terms of changes in temperature, microstructure, composition, and/or orientation. Materials used in the SiC-Mullite study consisted of single crystal SiC whiskers (prepared from rice hulls or by the vapor-liquid-solid process) dispersed within a polycrystalline mullite matrix. During measurement of thermal diffusivity, the samples were heated to l500°C and cooled back to room temperature. No hysteresis occurred. However, both thermal diffusivity and conductivity exhibited maximum values at room temperatures, perpendicular to the hot pressing direction, at high volume percentages of SiC whiskers, and when VLS whiskers were employed. The SiC-SiC samples consisted of a crossweave of polycrystalline SiC fibers that were coated with phenolic resin and surrounded by a chemically-vapor-deposited matrix of SiC. The two types of samples examined were prepared with different amounts of resin. The matrices of the high resin samples were found to be dominated by the presence of char. Samples were cycled to 1000, 1400, and l800°C; hysteresis occurred on some of the cycles. Thermal diffusivity was highest parallel to one set of fibers. These results allow the qualitative tailoring of the heat flow properties of these ceramic composites, for particular applications, and set forth limitations on the use of the SiC-SiC composites at high temperatures. / Master of Science