The electric field effect on magnetic anisotropy was studied in an ultrathin Fe(001) monocrystalline layer sandwiched between Cr buffer and MgO tunnel barrier layers, mainly through post-annealing temperature and measurement temperature dependences. A large coefficient of the electric field effect of more than 200 fJ/Vm was observed in the negative range of electric field, as well as an areal energy density of perpendicular magnetic anisotropy (PMA) of around 600 uJ/m2. More interestingly, nonlinear behavior, giving rise to a local minimum around +100 mV/nm, was observed in the electric field dependence of magnetic anisotropy, being independent of the post-annealing and measurement temperatures. The insensitivity to both the interface conditions and the temperature of the system suggests that the nonlinear behavior is attributed to an intrinsic origin such as an inherent electronic structure in the Fe/MgO interface. The present study can contribute to the progress in theoretical studies, such as ab initio calculations, on the mechanism of the electric field effect on PMA.