Based on a previously developed mathematical model describing the behavior of the window of a multi-kilowatt laser with an unstable cavity, the case of a two-component output window is considered. The two-component window consists of a transparent annular polycrystalline diamond and a central opaque area, separated by a plastic vacuum gasket. To reduce the heat load, the central opaque part is equipped with a cooler. Numerical calculations of thermomechanical processes for such windows used in high-power CO2 lasers are carried out. The mathematical model used for the calculations consists of three parts: thermophysical, mechanical, and optical. The advantages of the two-component design with a cooler being used with a multi-kilowatt gas laser are demonstrated. The dependences of the maximum admissible output radiation power, temperature distribution, and mechanical stresses on the window thickness are obtained. Conditions under which such an output window should not only successfully withstand the extreme radiation loads, but also ensure the minimum possible divergence of the outgoing radiation are considered.