By performing a two-step coordinate transformation, an N-sided polygonal bifunctional thermal device with nonsingular homogeneous material parameters is proposed based on transformation thermodynamics. The presented device could function as not only a concentrator with heat flux concentration effect, but also an illusion device with a scattering amplification effect. Moreover, to further eliminate the anisotropy of thermal conductivity tensors, multilayer realization of the device through isotropic materials is also investigated. The effectiveness of the design method and the performance of the devices are validated by the full-wave simulations. This work paves a new way for the design of easy-to-implement bifunctional devices and has broad application prospects in such fields as thermal-energy harvesting and thermal camouflage.