We observe spin transfer within a nondegenerate heteronuclear spinor atomic gas comprising a small 7Li population admixed with a 87Rb bath, with both elements in their F=1 hyperfine spin manifolds. Prepared in a nonequilibrium initial state, the 7Li spin distribution evolves through incoherent spin-changing collisions toward a steady-state distribution. We identify and measure the cross sections of all three types of spin-dependent heteronuclear collisions, namely the spin-exchange, spin-mixing, and quadrupole-exchange interactions, and find agreement with predictions of heteronuclear 7Liβ87Rb interactions at low energy. Moreover, we observe that the steady state of the 7Li spinor gas can be controlled by varying the composition of the 87Rb spin bath with which it interacts.