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We present an analysis of a diffusion-cooled hot-electron bolometer in the limiting case of a weak thermalization of non-equilibrium quasiparticles. We propose a new model relying on the non-thermal suppression of the superconducting energy gap by excess quasiparticles. Using material parameters typical for Al, we evaluate performance of the bolometer in the heterodyne regime at terahertz frequencies. Estimates show that the mixer may have quantum limited noise temperature and a few tens of GHz bandwidth, while the required local oscillator power is in the /spl mu/W range due to in-effective suppression of the energy gap by quasiparticles with high energies.