By means of a diffusive description of spin-dependent thermal and electrical transport using Pauli-spin matrices, we analyze the spin-dependent transport mechanisms that determine the voltage response of a metallic spin valve to an ac temperature oscillation under steady current and the second-harmonic voltage response to spin-torque induced oscillations of the magnetization of the layers. We show the extent to which both measurements are sensitive to the relaxation of the transverse spin moment. The simulations of these signals suggest an experimental protocol to characterize the decay of the spin-accumulation precession due to s-d interaction in ferromagnets.