The coupling of spin and heat gives rise to new physical phenomena in nanoscale spin devices. In particular, spin-transfer torque (STT) driven by thermal transport provides a new way to manipulate local magnetization. We quantify thermal STT in metallic spin-valve structures using an intense and ultrafast heat current created by picosecond pulses of laser light. Our result shows that thermal STT consists of demagnetization-driven and spin-dependent Seebeck effect (SDSE)-driven components; the SDSE-driven STT becomes dominant after 3 ps. The sign and magnitude of the SDSE-driven STT can be controlled by the composition of a ferromagnetic layer and the thickness of a heat sink layer.