This work provides an evaluation of the behavior of a planar circular solid oxide fuel cell stack with an integrated air preheater fed with hydrogen at the anode and air at the cathode under conditions of high fuel utilization. This evaluation is based on a simulation model, whose hypotheses and equations are presented and discussed, together with model validation. Indeed, it has been shown that the simulation results compare favorably with the experimental data of temperature distribution and I-V characteristics at low fuel utilization. Having ascertained the reliability of the model, the simulation results obtained at high fuel utilization are presented and discussed. I-V curves show an almost linear behavior up to fuel utilization factors above 80%. For higher utilizations, the slopes of the curves increase due to an increase of anodic polarization resistance, due to both activation effects and diffusion limitations in the electrode regions underneath the ribs of the gas distributor; on the contrary, diffusion limitations in the regions underneath the gas channels have been demonstrated to be negligible. The results for temperature distributions at high fuel utilization are discussed as well, indicating that the benefit of solid oxide fuel cells with an integrated air preheater, i.e., an almost even distribution of solid temperature on the cell plane, is still valid at high hydrogen utilization factors.