Cloaks can protect objects without disturbing heat signatures outside cloaks, and hence, objects are invisible to outside detection. However, cloaks themselves are visible to inside detection because they possess different heat signatures from the outside. This fact limits applications. Here, we solve this problem in thermotics by developing a different theory and then propose the scheme of thermal supercavity, a cavity without disturbing heat signatures outside. We investigate different supercavities with various shapes in two or three dimensions and validate the desired effects by simulations and experiments. We further design the scheme of super-invisibility which makes the cavity itself also invisible to inside detection. Moreover, our scheme simplifies the complicated parameters of non-circle shaped cloaks, which requires only two natural materials with a simple layer structure. Our work is useful for achieving new kinds of thermal devices, including thermal camouflage and designing similar supercavities in magnetostatics, electrostatics, particle diffusion, etc.