  We analytically derive the transport tensor of thermal conductivity in an
ultracold, but not yet quantum degenerate, gas of Bosonic lanthanide atoms
using the Chapman-Enskog procedure. The tensor coefficients inherit an
anisotropy from the anisotropic collision cross section for these dipolar
species, manifest in their dependence on the dipole moment, dipole orientation,
and $s$-wave scattering length. These functional dependencies open up a pathway
for control of macroscopic gas phenomena via tuning of the microscopic atomic
interactions. As an illustrative example, we analyze the time evolution of a
temperature hot-spot which shows preferential heat diffusion orthogonal to the
dipole orientation, a direct consequence of anisotropic thermal conduction.
