The thermal contribution to the nonlinear refractive index of air at 1.064mum was measured with a high-finesse Fabry-Perot cavity and a 500-mW cw laser beam. At room temperature and pressure, the nonlinear refractive-index coefficient of air was found to be n(2)((th))=(-1.9+/-0.2)x10 (-14) cm(2)/W for a beam waist radius of 0.23 mm and was found to be independent of the relative humidity. The thermal nonlinearities of N(2) , O(2) , and CO(2) were also measured, and it was found that the dominant contribution to air is its O(2) content.