We investigate the spin-Nernst effect in time-reversal-invariant topological superconductors, and show that it provides smoking-gun evidence for helical Cooper pairs. The spin-Nernst effect stems from asymmetric, in spin space, scattering of quasiparticles at nonmagnetic impurities, and generates a transverse spin current by the temperature gradient. Both the sign and the magnitude of the effect sensitively depend on the scattering phase shift at impurity sites. Therefore the spin-Nernst effect is uniquely suitable for identifying time-reversal-invariant topological superconducting orders.