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Conductivity of methylammonium lead triiodide (MAPbI3) perovskite was measured on different mesoporous metal oxide scaffolds: TiO2, Al2O3, and ZrO2, as a function of incident light irradiation and temperature. It was found that MAPbI3 exhibits intrinsic charge separation, and its conductivity stems from a majority of free charge carriers. The crystal morphology of the MAPbI3 was found to significantly affect the photoconductivity, whereas in the dark the conductivity is governed by the perovskite in the pores of the mesoporous scaffold. The temperature-dependent conductivity measurements also indicate the presence of states within the band gap of the perovskite. Despite a relatively large amount of crystal defects in the measured material, the main recombination mechanism of the photogenerated charges is bimolecular (band-to-band), which suggests that the defect states are rather inactive in the recombination. This may explain the remarkable efficiencies obtained for perovskite solar cells prepared with wet-chemical methods.