Thermoelectric manipulation of the magnetization of a magnetic layered stack in which a low-Curie temperature magnet is sandwiched between two strong magnets (exchange spring device) is considered. Controllable Joule heating produced by a current flowing in the plane of the magnetic stack (CIP configuration) induces a spatial magnetic and thermal structure along the current flow --- a magneto-thermal-electric domain (soliton). We show that such a structure can experience oscillatory in time dynamics if the magnetic stack is incorporated into an electric circuit in series with an inductor. The excitation of these magneto-thermionic oscillations follow the scenario either of soft of hard instability: in the latter case oscillations arise if the initial perturbation is large enough. The frequency of the temporal oscillations is of the order of $10^5 div 10^7 s^{-1}$ for current densities $jsim 10^6 div 10^7 A/cm^3$.
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