The existence of a heat-driven spin torque is demonstrated using Co/Cu/Co spin valves embedded in metallic nanowires. Heat currents flowing in one direction or its opposite were obtained by heating optically one end or the other of the nanowires. The spin torque associated with the heat-driven spin current pushes the magnetization out of equilibrium, resulting in a change of the magnetoresistance, which is detected using a charge current small enough not to cause heating or induced fields of any significance. The giant magnetoresistance response to this torque peaks with the magnetic susceptibility, whereas the spurious signal coming from the temperature dependence of the resistance produces merely a field independent baseline.