Thermal contact between a round spring and an enclosing cylinder is never very good. Theoretically there is only a line of contact. As a result heat transfer is not usually through the spring. The spring serves primarily as a means of creating turbulence. The turbulence improves heat transfer from the cylinder to the air. In a design that I worked on many years ago we used a twisted piece of aluminum dropped into the pipe to enhance turbulence. Creating too much turbulence hurts heat transfer because it reduces the volume of air moving through that path. As with all engineering, it's a juggling act.