Wolf-Rayet stars are known to eject winds . Thus , when a Wolf-Rayet star explodes as a supernova , a fast , > 30 , 000 km/s , shock is expected to be driven through a wind . We study the signal expected from a fast supernova shock propagating through an optically thick wind , and find that the electrons behind the shock driven into the wind are cooled efficiently , by inverse Compton over soft photons that were deposited by the radiation mediated shock that crossed the star . Therefore , the bolometric luminosity is comparable to the kinetic energy flux through the shock , and the spectrum is found to be a power-law , which slope and frequency range depend on the number flux of soft photons available for cooling . Wolf-Rayet supernovae that explode through a thick wind have a high flux of soft photons , producing a flat spectrum , \nu F _ { \nu } = Const , in the X-ray range 0.1 \lesssim T \lesssim 50 keV . As the shock expands into an optically thin wind , the soft photons are no longer able to cool the shock that plows through the wind , and the bulk of the emission takes the form of a standard core-collapse supernova ( without a wind ) . However , a small fraction of the soft photons is upscattered by the shocked wind and produces a transient unique X-ray signature .