  We have studied thermally driven magnon spin transport (spin Seebeck effect,
SSE) in heterostructures of antiferromagnetic $\alpha$-$\mathrm{Cr_2O_3}$ and
Pt at low temperatures. Monitoring the amplitude of the local and nonlocal SSE
signals as a function of temperature, we found that both decrease with
increasing temperature and disappear above 100 K and 20 K, respectively.
Additionally, both SSE signals show a tendency to saturate at low temperatures.
The nonlocal SSE signal decays exponentially for intermediate injector-detector
separation, consistent with magnon spin current transport in the relaxation
regime. We estimate the magnon relaxation length of our
$\alpha$-$\mathrm{Cr_2O_3}$ films to be around 500 nm at 3 K. This short magnon
relaxation length along with the strong temperature dependence of the SSE
signal indicates that temperature-dependent inelastic magnon scattering
processes play an important role in the intermediate range magnon transport.
Our observation is relevant to low-dissipation antiferromagnetic magnon memory
and logic devices involving thermal magnon generation and transport.
