  Crystals and glasses differ by the amplitude and the temperature dependence
of their thermal conductivity. However, there are crystals known to display
glass-like thermal conductivity. Here, we show that EuTiO$_3$, a quantum
paraelectric known to order antiferromagnetically at 5.5 K, is one such system.
The temperature dependence of resistivity and Seebeck coefficient yield an
insulating band gap of $\sim 0.22$ eV. Thermal conductivity is drastically
reduced. Its amplitude and temperature dependence are akin to what is seen in
amorphous silica. Comparison with non-magnetic perovskite solids, SrTiO$_3$,
KTaO$_3$, and EuCoO$_3$, shows that what impedes heat transport are $4f$ spins
at Eu$^{2+}$ sites, which couple to phonons well above the ordering
temperature. Thus, in this case, superexchange and valence fluctuations, not
magnetic frustration, are the drivers of the glass-like thermal conductivity.
