Supersoft X-ray sources are stellar objects that emit X-rays with temperatures of about 1 million kelvin and luminosities well in excess of what can be produced by stellar coronae. It has generally been presumed that the objects in this class are binary star systems in which mass transfer leads to nuclear fusion on the surface of a white dwarf 1 . Classical novae—the runaway fusion events on the surfaces of white dwarfs—generally have supersoft phases, and it is often stated that the bright steady supersoft X-ray sources seen from white dwarfs accreting mass at a high rate are undergoing steady nuclear fusion 1 . Here, we report the discovery of a transient supersoft source in the Small Magellanic Cloud without any signature of nuclear fusion having taken place. This discovery indicates that the X-ray emission probably comes from a ‘spreading layer’ 2 —a belt on the surface of the white dwarf near the inner edge of the accretion disk in which a large fraction of the total accretion energy is emitted—and (albeit more tentatively) that the accreting white dwarf is relatively massive. We thus establish that the presence of a supersoft source cannot always be used as a tracer of nuclear fusion, in contradiction with decades-old consensus about the nature of supersoft emission.