An important factor in controlling invasive plant infestations is frequently the acceleration of the deterioration of their persistent seed bank, which is often associated with physical dormancy mechanisms. We hypothesized that breaking dormancy by heat would enhance the vulnerability of the nondormant seeds to hydrothermal stresses. The aim of the present study was to examine the effect of soil solarization treatments (heating the soil by means of polyethylene mulching) on buried Australian Acacia seeds, with emphasis on Acacia saligna L. The results of three field experiments indicate that soil solarization treatments caused an almost complete eradication of buried seeds of Acacia saligna and two other Australian Acacia species, Acacia murrayana and Acacia sclerosperma. The killing mechanism of solarization was further studied in laboratory experiments. We observed two phases of the heat-induced deterioration of seed persistence: breaking the dormancy of the seeds and exposing the “weakened seeds” to lethal temperatures. From an ecological perspective of conservation, the present study shows for the first time the possible utilization of solar energy, by means of soil solarization, for reducing persistent seed banks of invasive woody plants.