Fibrous ceramic structures are used in thermal insulators and filters in high‐temperature processes. Their mechanical properties are surprisingly complex, being governed by force fields transmitting in the net of fibers. Examining how the fibers link to each other sheds light to this quandary. Extent of linking is defined by the fiber free length (deep red), which is the distance between the closest contact points (green) of a fiber. Decrease of free length, as neighboring fibers (blue) develop contacts, explains why these structures turn rigid with heat. When analyzed with grit blasting, this can be used to discover the structure's thermal history.