The present work investigates the thermal aspects of a differentially heated porous square enclosure in the presence of an adiabatic block of different block sizes utilizing Darcy-Rayleigh number in the range of 1-10,000 with Darcy number 10(-2)-10(-6). Heatlines and Nusselt number, streamlines, and entropy generation are used for the analysis of heat transfer, flow circulation, and irreversibility production in the enclosure. The study reveals that the presence of an adiabatic block affects the heat transfer process severely, and three different zones of heat transfer are identified. These are namely the zone of heat transfer augmentation, the zone of heat transfer augmentation along with entropy generation reduction, and the zone of both heat transfer and entropy generation reduction. It is also found that the presence of an adiabatic block can enhance heat transfer up to a certain critical block size; thereafter, further increasing in block size reduces the heat transfer rate. An optimal block size where the heat transfer enhancement is maximum is observed to be smaller than the critical block size. The study demonstrates the analyses of heat transfer and entropy generation for a better thermal design of a system. This study is also extended for higher Prandtl number fluids.