  Considering metallic films at room temperature, we present the first
theoretical study of the spin Nernst and thermal Edelstein effects which takes
into account dynamical spin-orbit coupling, i.e., direct spin-orbit coupling
with the vibrating lattice (phonons) and impurities. This gives rise to two
novel processes, namely a dynamical Elliott-Yafet spin relaxation and a
dynamical side-jump mechanism. Both are the high-temperature counterparts of
the well-known $T = 0$ Elliott-Yafet and side-jump, central to the current
understanding of the spin Hall, spin Nernst and Edelstein effects at low $T$.
We consider the experimentally relevant regime $T > T_D$, with $T_D$ the Debye
temperature, as the latter is lower than room temperature in transition metals
such as Pt, Au and Ta typically employed in spin injection/extraction
experiments. We show that the interplay between intrinsic (Bychkov-Rashba type)
and extrinsic (dynamical) spin-orbit coupling yields a nonlinear $T$-
dependence of the spin Nernst and spin Hall conductivities.
