  We present the results of measurements of the thermal conductivity $\kappa$
of the spin S=1 chain compound AgVP_2S_6 in the temperature range between 2 and
300 K and with the heat flow directed either along or perpendicular to the
chain direction. The analysis of the anisotropy of the heat transport allowed
for the identification of a small but non-negligible magnon contribution
$\kappa_m$ along the chains, superimposed on the dominant phonon contribution
$\kappa_ph$. At temperatures above about 100 K the energy diffusion constant
D_E(T), calculated from the $\kappa_m(T)$ data, exhibits similar features as
the spin diffusion constant D_S(T), previously measured by NMR. In this regime,
the behaviour of both transport parameters is consistent with a diffusion
process that is caused by interactions inherent to one-dimensional S=1 spin
systems.
