The method comprises supplying, at a construction site, of a functional module comprising a hybrid cooler; verifying onsite the exploitation of the equipment of the functional module; mounting the functional module on a support structure; moving the structure to an exploitation site on the expanse of water. The verification involves passing a flow to be cooled through the air cooler of the hybrid cooler, the flow being cooled exclusively by a flow of air circulating through the air cooler of the hybrid cooler. The exploitation of hydrocarbons on the expanse of water involves the passage of a flow to be cooled through the water cooler of the hybrid cooling system, the flow being cooled by heat exchange with water taken from the expanse of water circulating through the water cooler.