Transformation optics based metamaterial thermal harvesting devices, which provides power and efficiency related advantages by manipulating and concentrating thermal fluxes, have attracted considerable research interests. The potential utilizations are significant for improving the energy conversion efficiencies in existing collecting technologies including heat storages, solar thermal collectors, full cells, etc. However, most of the current researches on thermal harvesting devices are mainly focused on continuous shape profiles based on the scattering cancellation. In this paper, we propose a novel method for fabricating desirable polygonal thermal harvesting devices with homogeneous and nonsingular parameters through linear mapping function. Four polygonal concentrating schemes with fewer kinds of natural materials filling inside the functional regions are demonstrated in transient states. The expected harvesting performances are achieved for each proposed polygonal scheme. Furthermore, the proposed thermal harvesting performances are investigated as a function of the dense degree of the medium-layer configurations. In general, this paper demonstrates a novel method for designing non-continuous shape polygon harvesting devices with corresponding validations. Improved concentrating behaviors would be achieved with denser medium configurations, implemented as appropriately arranged fractions. The findings could have potentials for designing novel transformation optics devices and providing improved energy conversion efficiencies in existing collecting technologies.