A new inverse Compton scattering scheme for production of high-energy Gamma-ray sources is proposed in which a Giga-electronvolt (GeV) electron beam is injected into a thermal hohlraum. It is found that by increasing the hohlraum background temperature, the scattered photons experience kinematic pileup, resulting in more monochromatic spectrum and smaller scattering angle. When a relativistic electron beam with energy 1 GeV and charge 10nC is injected into a 0.5 keV hohlraum, 80% of the scattered photons have energy above 0.5 GeV.