Spin-transfer torques, both reactive and dissipative, induced by temperature gradients in conducting ferromagnets are calculated microscopically for smooth magnetization textures. Temperature gradients are treated à la Luttinger by introducing a fictitious gravitational field that couples to the energy density. The thermal torque coefficients obtained by the Kubo formula contain unphysical terms that diverge towards zero temperature. Such terms are caused by equilibrium components and 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 that couples to the entropy rather than energy would solve the issue from the outset.