To further study the heat transfer process inside the functionally graded thermal barrier coatings (FGTBCs) beyond the companion part of the present paper concerning their radiative properties, this paper takes both conductive and radiative heat transfer into account and establishes a comprehensive heat transfer model considering both conductive and radiative heat transfer to estimate the thermal insulation performance of FGTBCs. Thermal conductivities of more than thirty yttria-stabilized zirconia (YSZ)/NiCoCrAlY FGTBC samples were determined based on their thermal diffusivities determined by the laser flash analysis. To predict the overall thermal insulation performance of 8YSZ/NiCoCrAlY FGTBCs, a comprehensive heat transfer model based on the two-flux method and multi-band model was built to solve the stationary temperature distribution and heat flux inside thermal barrier coatings (TBCs) and FGTBCs. Results indicate that FGTBCs show worse thermal insulation performance compared to conventional YSZ TBCs; we also investigated the influence of the number of layers. The temperature of engine blade is increased by 3050K if coated with an FGTBC instead of a conventional TBC. Conduction heat flux is significantly greater than radiative flux for both TBCs and FGTBCs. This paper gives a detailed analysis by simultaneously considering the heat conduction and thermal radiation in FGTBCs, which is helpful for achieving better thermal design of YSZ/NiCoCrAlY FGTBCs. Along with the Part I, this two-part article presents a deep and thorough study on the thermal insulation performance of YSZ/NiCoCrAlY FGTBCs. (C) 2019 Elsevier Ltd. All rights reserved.