  The magnonic spin Seebeck effect is a key element of spin caloritronic, a
field that exploits thermal effects for spintronic applications. Early studies
were focused on investigating the steady-state nonequilibrium magnonic spin
Seebeck current, and the underlying physics of the magnonic spin Seebeck effect
is now relatively well established. However, the initial steps of the formation
of the spin Seebeck current are in the scope of recent interest. To address
this dynamical aspect theoretically we propose here a new approach to the
time-resolved spin Seebeck effect. Our method exploits the supersymmetric
theory of stochastics and Ito - Stratonovich integration scheme. We found that
in the early step the spin Seebeck current has both nonzero transversal and
longitudinal components. As the magnetization dynamics approaches the
steady-state, the transversal components decay through dephasing over the
dipole-dipole reservoir. The time scale for this process is typically in the
sub-nanoseconds pointing thus to the potential of an ultrafast control of the
dynamical spin Seebeck during its buildup.
