Non-equilibrium process of combustion-wave propagation of thermite compositions (Mg/Fe2O3) inside the sealed steel tube have been investigated to study the burning rate at elevating pressure. Under confinement the hot gas-phase products, formed during thermite combustion result in considerable overpressure inside the tube that reverses the gas flow and leads to pressure-driven preheating effect of the burned-gas permeation. Convective origin of this preheating effect is discussed. The pressure-time dependency is obtained experimentally. The composition was pressed inside the steel tube in pellets; the size of each part was measured to obtain burning rate – pressure dependency. Both micro- and nanosized components were used to prepare thermite compositions under study. The significant difference in burning parameters of micron- and nanosized thermites is observed and analyzed. Based on obtained results, the combustion mechanism of thermites with the micro- and nanosized components is discussed.