  We complete measurements of interconversions among the full triad of thermal
gradients, charge currents, and spin currents in the topological insulator
Bi$_2$Se$_3$ by quantifying the efficiency with which thermal gradients can
generate transverse spin currents. We accomplish this by comparing the spin
Nernst magneto-thermopower to the spin Hall magnesistance for bilayers of
Bi$_2$Se$_3$/CoFeB. We find that Bi$_2$Se$_3$ does generate substantial
thermally-driven spin currents. A lower bound for the ratio of spin current to
thermal gradient is $J_s/\nabla_x T$ = (4.9 $\pm$ 0.9) $\times$ 10$^{6}$
($\hbar/2e$) A m$^{-2}$ / K $\mu$m$^{-1}$, and a lower bound for the magnitude
of the spin Nernst ratio is $-$0.61 $\pm$ 0.11. The spin Nernst ratio for
Bi$_2$Se$_3$ is the largest among all materials measured to date, 2-3 times
larger compared to previous measurements for the heavy metals Pt and W.
