  We study the spectrum of high frequency radiation emerging from mildly
dissipative photospheres of long-duration gamma-ray burst outflows. Building on
the results of recent numerical investigations, we assume that electrons are
heated impulsively to mildly relativistic energies by either shocks or magnetic
dissipation at Thomson optical depths of several and subsequently cool by
inverse Compton, scattering off the thermal photons of the photosphere. We show
that even in the absence of magnetic field and non-thermal leptons, inverse
Compton scattering produces power-law tails that extend from the peak of the
thermal radiation, at several hundred keV, to several tens of MeV, and possibly
up to GeV energies. The slope of the high-frequency power-law is predicted to
vary substantially during a single burst, and the model can easily account for
the diversity of high-frequency spectra observed by BATSE. Our model works in
baryonic as well as in magnetically dominated outflows, as long as the magnetic
field component is not overwhelmingly dominant.
