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Several past studies have described how absorption spectroscopy can be used to determine spatial temperature variations along the optical path by measuring the unique, nonlinear response to temperature of many molecular absorption transitions and performing an inversion. New laser absorption spectroscopy techniques are well-suited to this nonuniformity measurement, yet present analysis approaches use only isolated features rather than a full broadband spectral measurement. In this work, we develop a constrained spectral fitting technique called E"-binning to fit an absorption spectrum arising from a nonuniform environment. The information extracted from E"-binning is then input to the inversion approach from the previous paper in this series (Malarich and Rieker, JQSRT 107455) to determine the temperature distribution. We demonstrate this approach by using dual frequency comb laser measurements to resolve convection cells in a tube furnace. The recovered temperature distributions at each measurement height agree with an existing natural convection model. Finally, we show that for real-world measurements with noise and absorption model error, increasing the bandwidth and the number of measured absorption transitions may improve the temperature distribution precision. We make the fitting code publicly available for use with any broadband absorption measurement.