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The cooling method in fire suppression specifically focuses on reducing the temperature of the burning material to below its ignition temperature. This is essential because for combustion to occur, a material must reach a certain temperature that sustains the chemical reactions of fire. By applying water or other cooling agents, the heat is lowered, which not only quenches the flames but also prevents the potential for reignition. This method is fundamental in firefighting because it effectively removes one of the critical elements of the fire triangle: heat.

In contrast, inserting an object into the fire may not necessarily address the heat temperature or extinguish the flames effectively. Dispersing the flames does not directly cool the materials but may only move them around without reducing the temperature. Using fire-retarding agents plays a role in preventing the fire from spreading but doesn't primarily focus on reducing the immediate temperature of the burning material. Each of these methods serves different functions in fire suppression, but cooling specifically involves lowering the temperature to eliminate the fire's source of heat.