  Using the spin Seebeck effect (SSE), we study the propagation distance of
thermal spin currents inside a magnetic insulator thin film in the short-range
regime. We disambiguate spin currents driven by temperature and chemical
potential gradients by comparing the SSE signal before and after adding a
thermalization capping layer on the same device. We report that the measured
spin decay behavior near the heat source is well accounted for by a diffusion
model where the magnon diffusion length is in submicron range, \textit{i.e.}
two orders of magnitude smaller than previous estimates inferred from the
long-range behavior. Our results highlight the caveat in applying a diffusive
theory to describe thermal magnon transport, where a single decay length may
not capture the behavior on all length scales.
