Recent laboratory work has suggested that the rheology of the lower mantle may be Newtonian. We have studied the time-dependent dynamics of plumes interacting with a rheological interface separating an upper non-Newtonian mantle and a Newtonian lower mantle. Pulsating diapiric structures with fast time scales are promoted by the interaction of the rising plumes with this rheological boundary. Surface heat flow signals are discernible as pulses, which remain relatively stationary. They correlate well with the localized upwellings just below the surface. The presence of a mobile lithosphere from increasing the non-Newtonian power-law index helps to produce a large-scale circulation in the upper mantle which draws large hot patches away from nearby upwellings. In our calculations the resultant averaged effective viscosity of the non-Newtonian upper mantle is about two orders of magnitude lower than that of the Newtonian lower mantle. A viscously stratified Newtonian model produces more incoherent and broad-scale diapiric structures and is less efficient for generating sharply varying time-dependent thermal signatures.