Crude oil spill accidents cause extreme environmental damage, with huge economic costs that include the loss of oil resources. Despite the advances in conventional oil spill cleanup technology, such as dispersants, absorbents, and skimmers, there is still a need for more efficient solutions. In this study, we introduce a Joule-heated stearic acid/carbon nanotube-wrapped polyurethane sponge (SCPU) for rapid and all-weather recovery of leaked crude oil. SCPU is both hydrophobic and oleophilic and is electrically conductive. When 6 V were applied across the SCPU, the surface temperature increased to 146 °C within 70 s, which reduced the viscosity of crude oil and shortened the recovery time by over 99%. In addition, the Joule-heated SCPU can continuously recover crude oil floating on the water surface when connected to a peristaltic pump. This Joule-heated SCPU has a high crude oil adsorption capacity, a scalable preparation method, and is mechanically stable, and thus is expected to provide an efficient and practical solution for responding to crude oil spill accidents.