A method of installing at sea a double-walled preheated undersea pipe for transporting fluids, wherein for each new pipe section to be assembled to a pipe that is already installed at sea: the method involves preheating the inner wall unit element inside the outer wall unit element of the new pipe section; assembling the inner wall unit elements of the new pipe section to the inner wall of the pipe that is already installed at sea; assembling the outer wall unit element of the new pipe section to the outer wall of the pipe that is already installed at sea; lowering the new pipe section into the sea; and repeating the above for other new pipe sections to be assembled so as to prestress the pipe while it is being installed at sea.