  Thermal conductivities are routinely calculated in molecular dynamics
simulations by keeping the boundaries at different temperatures and measuring
the slope of the temperature profile in the bulk of the material, explicitly
using Fourier's law of heat conduction. Substantiated by the observation of a
distinct linear profile at the center of the material, this approach has also
been frequently used in superdiffusive materials, such as nanotubes or polymer
chains, which do not satisfy Fourier's law at the system sizes considered. It
has been recently argued that this temperature gradient procedure yields worse
results when compared with a method based on the temperature difference at the
boundaries -- thus taking into account the regions near the boundaries where
the temperature profile is not linear. We study a realistic example,
nanocomposites formed by adding boron nitride nanotubes to a polymer matrix of
amorphous polyethylene, to show that in superdiffusive materials, despite the
appearance of a central region with a linear profile, the temperature gradient
method is actually inconsistent with a conductivity that depends on the system
size, and, thus, it should be only used in normal diffusive systems.
