  The emergence of symmetry-breaking orders such as ferromagnetism and the weak
interlayer bonding in van der Waals materials, offers a unique platform to
engineer novel heterostructures and tune transport properties like thermal
conductivity. Here, we report the experimental and theoretical study of the
cross-plane thermal conductivity, $\kappa_\perp$, of the van der Waals 2D
ferromagnet Fe$_3$GeTe$_2$. We observe a non-monotonic increase of
$\kappa_\perp$ with the thickness and a large suppression in
artificially-stacked layers, indicating a diffusive transport regime with
ballistic contributions. These results are supported by the theoretical
analyses of the accumulated thermal conductivity, which show an important
contribution of phonons with mean free paths between 10 and 200 nm. Moreover,
our experiments show a reduction of the $\kappa_\perp$ in the low-temperature
ferromagnetic phase occurring at the magnetic transition. The calculations show
that this reduction in $\kappa_\perp$ is associated with a decrease in the
group velocities of the acoustic phonons and an increase in the phonon-phonon
scattering of the Raman modes that couple to the magnetic phase. These results
demonstrate the potential of van der Waals ferromagnets for thermal transport
engineering.
