  In many physical situations in which many-body assemblies exist at
temperature $T$, a characteristic quantum-mechanical time scale of
approximately $\hbar/k_{B}T$ can be identified in both theory and experiment,
leading to speculation that it may be the shortest meaningful time in such
circumstances. When this behaviour is investigated by probing the scattering
rate of strongly interacting electrons in metals, it is clear that in some
cases only electron-electron scattering can be its cause, while in others it
arises from high-temperature scattering of electrons from quantised lattice
vibrations, i.e. phonons. In metallic oxides, which are among the most studied
materials, analysis of electrical transport does not satisfactorily identify
the relevant scattering mechanism at 'high' temperatures near room temperature.
We employ a contactless optical method to measure thermal diffusivity in two
Ru-based layered perovskites, Sr$_3$Ru$_2$O$_7$ and Sr$_2$RuO$_4$, and use the
measurements to extract the dimensionless Lorenz ratio. By comparing our
results to the literature data on both conventional and unconventional metals
we show how the analysis of high-temperature thermal transport can both give
important insight into dominant scattering mechanisms, and be offered as a
stringent test of theories attempting to explain anomalous scattering.
