  We present experimental measurements of the thermal boundary conductance
(TBC) from $77 - 500$ K across isolated heteroepitaxially grown ZnO films on
GaN substrates. These data provide an assessment of the assumptions that drive
the phonon gas model-based diffuse mismatch models (DMM) and atomistic Green's
function (AGF) formalisms for predicting TBC. Our measurements, when compared
to previous experimental data, suggest that the TBC can be influenced by long
wavelength, zone center modes in a material on one side of the interface as
opposed to the "vibrational mismatch" concept assumed in the DMM; this
disagreement is pronounced at high temperatures. At room temperature, we
measure the ZnO/GaN TBC as $490\lbrack +150, -110\rbrack$ MW m$^{-2}$ K$^{-1}$.
The disagreement among the DMM and AGF and the experimental data these elevated
temperatures suggests a non-negligible contribution from additional modes
contributing to TBC that not accounted for in the fundamental assumptions of
these harmonic formalisms, such as inelastic scattering. Given the high quality
of these ZnO/GaN interface, these results provide an invaluable critical and
quantitive assessment of the accuracy of assumptions in the current state of
the art of computational approaches for predicting the phonon TBC across
interfaces.
