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The optimization of the Yb:YAG gain medium and absorbing clad parameters was investigated for efficient heat removal in cryogenically-cooled multislab amplifiers operating in the kilowatt average power range (100 J/10 Hz). The 3-D distributions of temperature, stress, strain, and birefringence were calculated by a finite element analysis. Based on these data, the space-resolved optical path difference and depolarization losses were determined considering eight slabs, two laser heads, and four passes. We have found that a combination of properly designed (doping/width) index matching material and helium cryogenic cooling leads to a quasi-constant transverse temperature distribution in the pump area and a very small axial thermal gradient in the slab. It is shown that the resulting thermally induced phase aberrations, stresses, and average depolarization are rendered insignificant.