Transonic discs with accretion rates relevant to intrinsically bright Galactic X-ray sources ( L \approx 10 ^ { 38 } – 10 ^ { 39 } { erg s } ^ { -1 } ) exhibit a time dependent cyclic behaviour due to the onset of a thermal instability driven by radiation pressure . In this paper we calculate radiation spectra emitted from thermally-unstable discs to provide detailed theoretical predictions for observationally relevant quantities . The emergent spectrum has been obtained by solving self-consistently the vertical structure and radiative transfer in the disc atmosphere . We focus on four particular stages of the disc evolution , the maximal evacuation stage and three intermediate stages during the replenishment phase . The disc is found to undergo rather dramatic spectral changes during the evolution , emitting mainly in the 1–10 keV band during outburst and in the 0.1–1 keV band off-outburst . Local spectra , although different in shape from a blackbody at the disc effective temperature , may be characterized in terms of a hardening factor f . We have found that f is rather constant both in radius and in time , with a typical value \sim 1.65 .