  We have studied the longitudinal spin Seebeck effect (LSSE) in the layered
ferromagnetic insulators CrSiTe$_3$ and CrGeTe$_3$ covered by Pt films in the
measurement configuration where spin current traverses the ferromagnetic Cr
layers. The LSSE response is clearly observed in the ferromagnetic phase and,
in contrast to a standard LSSE magnet Y$_3$Fe$_5$O$_{12}$, persists above the
critical temperatures in both CrSiTe$_3$/Pt and CrGeTe$_3$/Pt samples. With the
help of a numerical calculation, we attribute the LSSE signals observed in the
paramagnetic regime to exchange-dominated interlayer transport of in-plane
paramagnetic moments reinforced by short-range ferromagnetic correlations and
strong Zeeman effects.
