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A new frequency domain hot-electron bolometer (HEB) mixer model is described, which takes into account the non-uniform temperature distribution found in superconducting diffusion-cooled devices. In this model the bolometer is discretized into a finite number of segments, and the non-linear large signal response to local oscillator and DC heating is found by an iterative algorithm. A frequency-domain coupling matrix is introduced to represent small-signal modulations around the large-signal values of temperatures and heat flows inside the device. The coupling matrix and a Norton representation of the mixer DC and intermediate frequency (IF) circuit allows the mixer conversion to be calculated.