  Spin-transfer torques induced by temperature gradients in conducting
ferromagnets are calculated microscopically for smooth magnetization textures.
Temperature gradients are treated a la Luttinger by introducing a fictitious
gravitational field that couples to the energy density. The thermal torque
coefficients obtained by the Kubo formula contain divergences caused by
equilibrium components that should be subtracted before applying the
Einstein-Luttinger relation. Only by following this procedure a familiar
Mott-like formula is obtained for the dissipative spin-transfer torque. The
result indicates that a fictitious field coupled to the entropy rather than
energy would solve the issue from the outset.
