This study describes the application of transient thermal analysis to study the diffusion of heat within materials commonly used to assess the ignition propensity of cigarettes. The propensity of cigarettes to ignite upholstered furnishings is typically assessed by exposing materials, designed to approximate the thermal response of soft furnishings, to smoldering cigarette coals. NIST* prescribes two methods that use different types and combinations of materials. The first method employs cotton duck fabrics of different densities in combination with polyurethane foam and, in one case, polypropylene film. Failure of a cigarette is defined as transition of the substrate to flaming combustion or propagation of a substrate char zone beyond a specified distance from the axis of the cigarette. Extinction of a cigarette prior to flaming combustion or a spreading char is considered a non-ignition. The second NIST method prescribes the use of layered cellulosic filter paper. In this case, a success is defined as an extinction of the cigarette. In both methods processes involving initial heating of the material, volatilization, pyrolysis, charring, smoldering and/or transition to flaming combustion are quite complex. The rate of spreading and the geometry of the various reaction zones depend on heat flux from the coal, the substrate properties, the geometry and combination of substrates, ion content, and oxygen availability. At threshold temperatures specific to each material, the substrate properties become time dependent and evolve in accordance with the kinetics associated with volatilization, pyrolysis, combustion, and mass transfer. While these factors become important at later times, it is the heat transport at the leading edge of the thermal front that determines if and when the materials reach these threshold temperatures. This talk describes the experimental technique used to characterize the heat diffusion within several substrate materials. The observed thermal responses will be discussed in the context of specific heat, density, thermal conductivity, and heterogeneity.* Test Methods for Quantifying the Propensity of Cigarettes to Ignite Soft Furnishings, U.S. Department of Commerce Technology Administration, National Institute of Standards and Technology, NIST special publications 851, August 1993.