Thermal conductivity, λ, and thermal diffusivity, a, of porous refractory oxide ceramic materials vary in a complicated manner with temperature, T, and gas pressure, p, which cannot be explained on the basis of known classical heat-transfer mechanisms in porous materials, which are conduction in solid and gas phases, gas convection, and heat radiation. This abnormal behaviour includes: (i) different T dependence of λ at atmospheric and at low pressure; (ii) at high T, thermal diffusivity measured in vacuum can exceed this property measured at atmospheric pressure; (iii) λ and a can depend on the measurement method. In order to explain the peculiarities of behaviour of λ and a, two additional groups of heat-transfer mechanisms are reviewed, including heterogeneous heat and mass transfer processes occurring in pores and in cracks, and microstructural changes due to nonuniform thermal expansion of particles and grains. A physicomathematical model for calculation of λ and a of porous ceramic materials and their dependence on T and p is described, which incorporates the above heat-transfer mechanisms. This model is used to explain and correlate the extensive experimental data for λ and a collected over wide ranges of T and p by steady-state and transient methods. It is shown that λ may increase with T at low and atmospheric pressure as a result of the microstructural changes due to the thermal expansion mismatch between the different grains. The increase of a with T in vacuum, and the dependence of λ and a on the measurement method, observed for chrome-magnesite and other refractories, can be attributed to heterogeneous reactions on the pore surfaces, accompanied by gas emission.