Thermal protection systems (TPS) are employed for spacecraft to survive high temperature conditions during atmospheric re-entry. For space shuttle type re-entries, the use of ceramic tiles shield the payload from exposure to these high heat fluxes. Recent research into the use of low-density materials, such as alumina foams, brings its own scientific challenges, of which understanding internal heat transfer is one. To this end, the exact 3D geometry of their complex porous structures, before and after plasma torch heating, is obtained by tomography and used in direct pore-level simulations to numerically calculate their effective heat transfer properties. Morphological characterisation is conducted via two-point correlation functions and mathematical morphology operations. Porosity and hydraulic pore diameter are seen to increase from the pre-heating (virgin) to the post-heating (charred) sample. Collision-based Monte Carlo methods are then used for radiative heat transfer characterisation. A decrease in extinction coefficient is noted between the virgin and charred samples. Both samples exhibit a large backward scattering peak for diffusely reflecting surfaces.