We report on the characterization of silica aerogel thermal optical nonlinearity, obtained by z-scan technique. The results show that typical silica aerogels have nonlinear optical coefficient similar to that of glass $(≃ 10^{-12} $m$^2/$W), with negligible optical nonlinear absorption. The non\-li\-near coefficient can be increased to values in the range of $10^{-10} $m$^2/$W by embedding an absorbing dye in the aerogel. This value is one order of magnitude higher than that observed in the pure dye and in typical highly nonlinear materials like liquid crystals. ; Comment: 5 pages, 5 figures, Published by AIP Publishing