We explore layered strongly correlated materials as a platform to identify and control unconventional heat transfer phenomena. We demonstrate that these systems can be tailored to sustain a wide spectrum of heat transport regimes, ranging from ballistic, to hydrodynamic all the way to diffusive. Within the hydrodynamic regime, wave-like temperature oscillations are predicted up to room temperature. Temperature waves have a purely electronic origin, stemming from the existence of two components in the electronic system, each one thermalized at different temperatures. The interaction strength can be exploited as a knob to control the dynamics of temperature waves as well as the onset of different thermal transport regimes. The present results pave the way to transition-metal oxide heterostructures as building blocks for nanodevices exploiting the wave-like nature of heat transfer on the picosecond time scale.