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We develop a detailed kinetics model for Yb:YAG operating at any temperature and derive expressions for the heat, fluorescence, and lasing power densities and fractions, using a theoretical framework that includes conservation of ions (and power), saturation of the laser and pump beams, and a description of Boltzmann heating and cooling in the upper laser manifold. In addition, we introduce an equation that allows the fluorescence and lasing fractions and power densities to be easily calculated for any value of the extraction efficiency. The model is applied to Yb:YAG lasers operating at 295 and 77 K. We find that the heat fractions at room temperature for no lasing and for complete laser saturation are significantly less than those previously reported, while at 77 K the heat fractions are larger than at room temperature and close to previously reported values. We show, for the first time to our knowledge, that the heat fraction is not constant but varies significantly in the radial direction, leading to a radially dependent phase distortion.