Intense solar irradiation, radiative cooling to outer space, and internal heat generation determine the equilibrium temperature of a spacecraft. The balance between the solar absorption and thermal emittance of the surface is therefore crucial, in particular for autonomous parts directly exposed to the solar radiation and thermally insulated from the main thermal mass of the spacecraft. The material composition but also the coating thickness are found to influence the equilibrium temperature of an object in space. In this paper we report on a systematic search for a suitable composition and thickness of TixAlyNz alloy coatings prepared by reactive, unbalanced magnetron sputtering from targets consisting of differently sized titanium and aluminum sectors. The films were deposited on glass, glassy carbon, aluminum sheet metal, and on sputtered aluminum and TixAl(1-x) films on glass. The stoichiometry and sheet resistance of the films was determined with Rutherford backscattering and four-point probe measurements respectively. Reflectance spectra for the visible and infrared spectral ranges were used to obtain average solar absorptance and thermal emittance values used in model calculations of the equilibrium temperature. Neglecting internal heat contributions, the lowest calculated equilibrium temperature in orbit around the Earth, 32.5 degrees C, was obtained for a 505-nm-thick Ti0.14Al0.47N0.40-film.