We report on the unusual behavior of the in-plane thermal conductivity ($\ka$) and torque ($τ$) response in the Kitaev-Heisenberg material $α$-RuCl$_3$. $\ka$ shows a striking enhancement with linear growth beyond $H = 7$ T, where magnetic order disappears, while $τ$ for both of the in-plane symmetry directions shows an anomaly at the same field. The temperature- and field-dependence of $\ka$ are far more complex than conventional phonon and magnon contributions, and require us to invoke the presence of unconventional spin excitations whose properties are characteristic of the field-induced spin-liquid phase related to the enigmatic physics of the Kitaev model. ; Comment: 6 pages,4 figures