  We show that the centroid molecular dynamics (CMD) method provides a
realistic way to calculate the thermal diffusivity $a=\lambda/\rho c_{\rm V}$
of a quantum mechanical liquid such as para-hydrogen. Once $a$ has been
calculated, the thermal conductivity can be obtained from $\lambda=\rho c_{\rm
V}a$, where $\rho$ is the density of the liquid and $c_{\rm V}$ is the
constant-volume heat capacity. The use of this formula requires an accurate
quantum mechanical heat capacity $c_{\rm V}$, which can be obtained from a path
integral molecular dynamics simulation. The thermal diffusivity can be
calculated either from the decay of the equilibrium density fluctuations in the
liquid or by using the Green-Kubo relation to calculate the CMD approximation
to $\lambda$ and then dividing this by the corresponding approximation to $\rho
c_{\rm V}$. We show that both approaches give the same results for liquid
para-hydrogen and that these results are in good agreement with experimental
measurements of the thermal conductivity over a wide temperature range. In
particular, they correctly predict a decrease in the thermal conductivity at
low temperatures -- an effect that stems from the decrease in the quantum
mechanical heat capacity and has eluded previous para-hydrogen simulations. We
also show that the method gives equally good agreement with experimental
measurements for the thermal conductivity of normal liquid helium.
