  The impact of variable material properties, such as temperature-dependent
thermal conductivity and dynamical viscosity, on the dynamics of a fully
compressible turbulent convection flow beyond the anelastic limit are studied
in the present work by two series of three-dimensional direct numerical
simulations in a layer of aspect ratio 4 with periodic boundary conditions in
both horizontal directions. One simulation series is for a weakly stratified
adiabatic background, one for a strongly stratified one. The Rayleigh number is
$10^5$ and the Prandtl number is 0.7 throughout this study. The temperature
dependence of material parameters is imposed as a power law with an exponent
$\beta$. It generates a superadiabaticity $\varepsilon(z)$ that varies across
the convection layer. Central statistical quantities of the flow, such as the
mean superadiabatic temperature, temperature and density fluctuations, or
turbulent Mach numbers are compared in the form of horizontal plane-time
averaged profiles. It is found that the additional material parameter
dependence causes systematic quantitative changes of all these quantities, but
no qualitative ones. A growing temperature power law exponent $\beta$ also
enhances the turbulent momentum transfer in the weak stratification case by
40\%, it reduces the turbulent heat transfer by up to 50\% in the strong
stratification case.
