We present mid-infrared spectrophotometric results obtained with the ISO on the peculiar X-ray binary Cygnus X-3 in quiescence, at orbital phases 0.83 to 1.04. The 2.4-12 microns continuum radiation observed with ISOPHOT-S can be explained by thermal free-free emission in an expanding wind with, above 6.5 microns, a possible additional black-body component with temperature T ~ 250 K and radius R ~ 5000 solar radii at 10 kpc, likely due to thermal emission by circumstellar dust. The observed brightness and continuum spectrum closely match that of the Wolf-Rayet star WR 147, a WN8+B0.5 binary system, when rescaled at the same 10 kpc distance as Cygnus X-3. A rough mass loss estimate assuming a WN wind gives ~ 1.2 10^{-4} M(sun)/yr. A line at ~ 4.3 microns with a more than 4.3 sigma detection level, and with a dereddened flux of 126 mJy, is interpreted as the expected He I 3p-3s line at 4.295 microns, a prominent line in the WR 147 spectrum. These results are consistent with a Wolf-Rayet-like companion to the compact object in Cygnus X-3 of WN8 type, a later type than suggested by earlier works.
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