  Transonic discs with accretion rates relevant to intrinsically bright
Galactic X-ray sources ($L\approx 10^{38}$-$10^{39} {\rm erg s}^{-1}$) 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 $\sim 1.65$.
