We report positron-lifetime measurements in void-containing aluminum samples, which show strong temperature dependence for the positron trapping probability. A theory is presented for the positron motion and trapping in a three-dimensional array of large voids, which compares favorably with the experimental data. It is shown that at low temperatures the trapping is transition limited and strongly temperature dependent with a crossover to diffusion-limited and weakly-temperature-dependent behavior at high temperatures.