Large heat currents are obtained in Co/Cu/Co spin valves positioned at the middle of Cu nanowires. The second harmonic voltage response to an applied current is used to investigate the effect of the heat current on the switching of the spin valves. Both the switching field and the magnitude of the voltage response are found to be dependent on the heat current. These effects are evidence for a thermal spin-transfer torque acting on the magnetization and are accounted for by a thermodynamic model in which heat, charge and spin currents are linked by Onsager reciprocity relations.