  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--both with first-principles predictions based on the Wigner
transport equation and with thermoreflectance experiments--that the dominant
transport mechanisms of crystals (particle-like propagation) and glasses
(wave-like tunnelling) can coexist and compensate in materials with crystalline
bond order and nearly glassy bond geometry. We demonstrate that ideal
compensation emerges in a sample of silica in the form of tridymite, carved
from a meteorite found in Steinbach (Germany) in 1724, and yields a
"propagation-tunneling-invariant" (PTI) conductivity that is independent from
temperature and intermediate between the opposite trends of $\alpha$-quartz
crystal and silica glass. We show how such PTI conductivity occurs in the
quantum regime below the Debye temperature, and can largely persist at high
temperatures in a geometrically amorphous tridymite phase found in refractory
bricks fired for years in furnaces for steel smelting. Last, we discuss
implications to heat transfer in solids exposed to extreme temperature
variations, ranging from planetary cooling to heating protocols to reduce the
carbon footprint of industrial furnaces.
