We report the synthesis and characterization of thermite composites consisting of Al nanoparticles and three dimensionally-ordered macroporous (3DOM) CuO. The pores of 3DOM CuO have size ranging between 190 nm and 320 nm and size dispersion lower than 10%, while 70 nm Al particles we used in this study are dispersed uniformly over the entire composite structures. Both the size uniformity and homogeneous mixing enable quantitative correlation between structures and thermite reaction characteristics. Ignition of the thermite composites in a closed chamber initiates thermite reactions, and the combustion kinetics is recorded in terms of the transient pressure changes. Contrary to a premise that small CuO pores would result in mixing with Al nanoparticles at a smaller length scale and hence higher pressurization rate, 3DOM CuO with pore size smaller than 240 nm exhibits gradually lower pressurization rate as pore size decreases. It turns out that pressurization rate has the highest value when the pore size of CuO is about 240 nm. The size dependence indicates that two different pathways, solid-state and gaseous diffusion, account for oxygen transfer from CuO to Al in the thermite composites. With the pore size of CuO larger than 240 nm, gas-phase diffusion predominates and pressurization rate increases as the size of the pores decreases. On the other hand, at small length scale, i.e., with CuO pore size smaller than 240 nm, condensed-phase diffusion is becoming a visibly more influential factor, reversing the size dependence. The size-dependence of the pressurization rate from thermite composites of Al nanoparticles and geometry-controlled 3DOM CuO reveals that the thermite reaction has the highest combustion rate at the smallest length scale where the gaseous diffusion still surpasses condensed-phase diffusion.