An influence of a spatial temperature modulation of the heat release/consumption at the interface on nonlinear convective flows in the 47v2 silicone oil - water system, has been investigated. Two types of boundary conditions on lateral walls: periodic boundary conditions corresponding to laterally infinite two-layer system and rigid heat-insulated lateral walls corresponding to the closed cavity, have been considered. It is shown that the spatial modulation can change the sequence of bifurcations and lead to the appearance of new oscillatory regimes. Specifically, pulsating traveling waves changing the direction of propagation, as well as regimes corresponding to period doubling, period-four and period-eight bifurcations, have been obtained.