  The lattice thermal conductivity ($\kappa$) of two ceramic materials, cerium
dioxide (CeO$_2$) and magnesium oxide (MgO), is computed up to 1500 K using
first principles and the phonon Boltzmann Transport Equation (PBTE) and
compared to time-domain thermoreflectance (TDTR) measurements up to 800 K.
Phonon renormalization and the four-phonon effect, along with high temperature
thermal expansion, are integrated in our \textit{ab initio} molecular dynamics
(AIMD) calculations. This is done by first relaxing structures and then fitting
to a set of effective force constants employed in a temperature-dependent
effective potential (TDEP) method. Both three-phonon and four-phonon scattering
rates are computed based on these effective force constants. Our calculated
thermal conductivities from the PBTE solver agree well with literature and our
TDTR measurements. Other predicted thermal properties including thermal
expansion, frequency shift, and phonon linewidth also compare well with
available experimental data. Our results show that high temperature softens
phonon frequency and reduces four-phonon scattering strength in both ceramics.
Compared to MgO, we find that CeO$_2$ has weaker four-phonon effect and
renormalization greatly reduces its four-phonon scattering rates.
