  The thermal conductivity of a $d=1$ lattice of ferromagnetically coupled
planar rotators is studied through molecular dynamics. Two different types of
anisotropies (local and in the coupling) are assumed in the inertial XY model.
In the limit of extreme anisotropy, both models approach the Ising model and
its thermal conductivity $\kappa$, which, at high temperatures, scales like
$\kappa\sim T^{-3}$. This behavior reinforces the result obtained in various
$d$-dimensional models, namely $\kappa \propto L\,
e_{q}^{-B(L^{\gamma}T)^{\eta}}$ where $e_q^z
\equiv[1+(1-q)z]^{\frac{1}{1-q}}\;(e_1^z=e^z)$, $L$ being the linear size of
the $d$-dimensional macroscopic lattice. The scaling law $\frac{\eta
\,\gamma}{q-1}=1$ guarantees the validity of Fourier's law, $\forall d$.
