A method which controls sedimentation occurring at a heat exchanger for cooling hydrodesulfurization/hydrocracking residue containing asphaltenes at a high content and thereby prevents fouling of the heat exchanger is disclosed. A method for preventing fouling of a heat exchanger for cooling hydrodesulfurization/hydrocracking residue, which injects flux oil into hydrodesulfurization/hydrocracking residue containing asphaltenes at 1% by mass or more, wherein the flux oil is at least one species of residue selected from the group consisting of crude vacuum distillation residue and fluidized catalytic cracking residue, and injected into the hydrodesulfurization/hydrocracking residue to control its actual sediment content at 0.2% by mass or less, determined in accordance with IP-375 is also disclosed.