Abstract: Based on two-dimensional high resolution hydrodynamic numerical simulation,  we study the mechanical and radiative feedback effects from the central AGN on the cosmological evolution of an isolated elliptical galaxy. Physical processes such as star formation and supernovae are considered. The inner boundary of the simulation domain is carefully chosen so that the fiducial Bondi radius is resolved and the accretion rate of the black hole is determined self-consistently. It is well-known that when the accretion rates are high and low, the central AGNs will be in cold and hot accretion modes, which correspond to the radiative and kinetic feedback modes, respectively. The emitted spectrum from the hot accretion flows is harder than that from the cold accretion flows, which results in a higher Compton temperature accompanied by a more efficient radiative heating. Such a difference of the Compton temperature between the two feedback modes, the focus of this study, has been neglected in previous works. Significant differences in the kinetic feedback mode are found as a result of the stronger Compton heating and accretion becomes more chaotic. More importantly, if we constrain models to correctly predict black hole growth and AGN duty cycle after cosmological evolution, we find that the favored model parameters are constrained: mechanical feedback efficiency diminishes with decreasing luminosity and X-ray Compton temperature increases with decreasing luminosity. We conclude that radiative feedback in the kinetic mode is much more important than previously thought.