  Within the spinor Boltzmann equation (SBE) formalism, we derived a
temperature dependent thermal spin-orbit torque based on local equilibrium
assumption in a system with Rashba spin-orbit interaction. If we expand the
distribution function of spinor Boltzmann equation around local equilibrium
distribution, we can obtain the spin diffusion equation from SBE, then the spin
transfer torque, spin orbit torque as well as thermal spin-orbit torque we seek
to can be read out from this equation. It exhibits that this thermal spin-orbit
torque originates from the temperature gradient of local equilibrium
distribution function, which is explicit and straightforward than previous
works. Finally, we illustrate them by an example of spin-polarized transport
through a ferromagnet with Rashba spin-orbit coupling, in which those torques
driven whatever by temperature gradient or bias are manifested quantitatively.
