Remediation of crude-oil spills is a global challenge. Conventional sorbents are inefficient for complete remediation due to the high viscosity of crude oil. However, heating crude oil can dramatically reduce viscosity, allowing efficient remediation. In this study, we demonstrate that polyurethane sponge wrapped with Ti₃C₂T_X MXene (Ti₃C₂T_X@PU) realizes fast and complete remediation of crude oil with the help of Joule heating or photothermal effects. Due to excellent photothermal properties and metal-like conductivity of Ti₃C₂T_X, Ti₃C₂T_X@PU can quickly adapt to the various conditions in practical applications with the synergistic effect of solar heating and Joule heating. The excellent heating capacity enables Ti₃C₂T_X@PU to absorb more than 40 times its own weight of crude oil in 20 min. This all-weather sorbent design provides a promising solution for the cleanup of viscous crude-oil spills.