Considering metallic films at room temperature, we present the first theoretical study of the spin Nernst and thermal Edelstein effects that takes into account dynamical spin-orbit coupling, i.e., direct spin-orbit coupling with the vibrating lattice (phonons) and impurities. This gives rise to a novel process, namely, a dynamical side-jump mechanism, and to dynamical Elliott-Yafet spin relaxation, never before considered in this context. Both are the high-temperature counterparts of the well-known T=0 side-jump and Elliott-Yafet, central to the current understanding of the spin Hall, spin Nernst and Edelstein (current-induced spin polarization) effects at low T. We consider the experimentally relevant regime T>TD, with TD 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.