The thermal conductivities of crystals and glasses vary strongly and with opposite trends upon heating, decreasing in crystals and increasing in glasses. Here, we show that the dominant conduction mechanisms of crystals (particle-like propagation) and glasses (wave-like tunneling) can compensate in materials with crystalline bond order and nearly glassy bond geometry, yielding a hybrid crystal-glass conductivity that is constant from the quantum to the classical regime (i.e., from below to above the Debye temperature). We showcase these arguments with a combined theoretical and experimental study on meteoritic silica (a tridymite carved from a sample found in Steinbach, Germany, in 1724) and on a geometrically amorphous tridymite phase found in refractory bricks used in furnaces for steel smelting. Our results prove that temperature-invariant conductivities are not limited to the classical regime, and pave the way to understand or control heat-transport phenomena in solids exposed to extreme temperature variations, ranging from planetary cooling to heating protocols to reduce the carbon footprint of industrial furnaces.