The characteristic pseudogap temperature T* in Bi2Sr2CaCu2O8 system has been systematically evaluated as a function of doping, especially focusing on its overdoped region, by measuring the out-of-plane resistivity under the magnetic fields. Overdoped samples have been prepared by annealing TSFZ-grown Bi2Sr2CaCu2O8 single crystals under the high oxygen pressures (990 kgf/cm2). At a zero field, the out-of-plane resistivity showed a metallic behavior down to Tc (= 62 K), while under the magnetic fields of over 3 T,it showed typical upturn behavior from around 65 K upon decreasing temperature. This result suggests that the pseudogap and superconductivity are different phenomena.