The high-temperature thermal insulation materials (TIM) are critical for aerospace technology. The more thermal insulation it is, the thinner TIM is needed. Here we show that, by stacking super-aligned carbon nanotube (SACNT) films together, SACNT-stacked films (SACNT-SF) can be obtained, which outperforms the traditional TIMs for a wide range of working temperatures. In vacuum, the effective thermal conductivity of SACNT-SF is only 0.004W/m·K at room temperature, and 0.03 W/m·K at 2600℃. Theoretical analysis indicates that the nanometer diameter of the carbon nanotube, the nanoporous and anisotropic structure and the ultra-low density of SACNT-SF, and the high extinction coefficient of sp2-carbon play critical roles in reducing heat conduction via solid skeletons, radiation, and gas medium. The SACNT-SF is nanometer thick and fully flexible, which can be continuously and freely winded on various shapes of surfaces, generating a conformal TIM for a broad spectrum of applications.