  We study thermal transport in a classical one-dimensional Heisenberg model
employing a discrete time odd even precessional update scheme. This dynamics
equilibrates a spin chain for any arbitrary temperature and finite value of the
integration time step $\Delta t$. We rigorously show that in presence of
driving the system attains local thermal equilibrium which is a strict
requirement of Fourier law. In the thermodynamic limit heat current for such a
system obeys Fourier law for all temperatures, as has been recently shown [A.
V. Savin, G. P. Tsironis, and X. Zotos, Phys. Rev. B 72, 140402(R) (2005)].
Finite systems, however, show an apparent ballistic transport which crosses
over to a diffusive one as the system size is increased. We provide exact
results for current and energy profiles in zero- and infinite-temperature
limits.
