Tri-layered PbZr0.53Ti0.47O3/CoFe2O4/PbZr0.53Ti0.47O3 (PZT/CFO/PZT) nanostructures have been reported to have the highest pyroelectric energy harvesting and electrocaloric effect. These nanostructures are magnetically active and the resultant 'giant' effects are considered to be governed by dynamic magneto-electric coupling. Therefore, it is of interest to investigate such nanostructures for thermomagnetic energy conversion and its corresponding magnetocaloric effect (MCE). In this context, the present study reveals that ferroelectric/magnetic/ferroelectric multilayered nanostructures of PZT/CFO/PZT can be used to achieve pyroelectric control over magnetization even in the absence of an applied electric field. Using the same phenomena, the coexistence of a 'giant' positive and a negative MCE is attained in the tri-layered PZT/CFO/PZT nanostructures for identical temperature ranges, but with different levels of applied magnetic field. Unlike conventional structural phase transitions based MCE effects, the present study demonstrates the possibility of obtaining a giant MCE simply by pyroelectric control of magnetism. The MCE entropy changes (ΔS(H)max = 1.5 J kg-1 K-1 for inverse MCE and 18.15 J kg-1 K-1 for positive MCE at 245 K) calculated using Maxwell equations are found to be as large as those reported for existing giant MCE systems. Moreover, our investigation of the thermomagnetic energy conversion in these nanostructures indicate that the tri-layer configuration also has a giant thermomagnetic energy conversion efficiency of 41% relative to that obtained using the Carnot cycle.