It's not the size/volume that matters, but the mass. Even with our limited science and technology, we have designs for interplanetary ships that drag hundreds of meters of radiator surface with them. It's not hard to imagine - and it has been imagined many times - a ship that consists of a core with a gigawatt-range powerplant, reaction mass, efficient engines, and kilometer-long radiators to dump the powerplant heat into space. If anything, based on our knowledge and assuming no magitech breakthroughs in space propulsion, you should expect interstellar ships to be large but light, maximizing surface area while minimizing mass.