Spacecrafts such as Stardust (NASA, 2006) are protected by an ablative Thermal Protection System (TPS) for their hypersonic atmospheric entry. A new generation of TPS material, called Phenolic Impregnated Carbon Ablator (PICA), has been introduced with the Stardust mission. This new generation of low density carbon-phenolic composites is now widely used in the aerospace industry. Complex heat and mass transfer phenomena coupled to phenolic pyrolysis and pyrolysis gas chemistry occur in the material during atmospheric entry. Computer programs, as the Porous material Analysis Toolbox based on OpenFoam (PATO) released open source by NASA, allow to study the material response. In this study, a non-intrusive Anchored Analysis of Variance (Anchored-ANOVA) method has been interfaced with PATO to perform low-cost sensitivity analysis on this problem featuring a large number of uncertain parameters. Then, a Polynomial-Chaos method has been employed in order to compute the statistics of some quantities of interest for the atmospheric entry of the Stardust capsule, by taking into account uncertainties on effective material properties and pyrolysis gas composition. This first study including pyrolysis gas composition uncertainties shows their key contribution to the variability of the quantities of interest.