The transport properties of MAPbI3 are analyzed within a tight-binding model. We find a strong Fröhlich interaction of electron and holes with the electrostatic potential induced by the longitudinal optical phonon modes. This potential induces a strong scattering and limits the electronic mobilities at room temperature to about 200 cm^{2}/V s. With additional extrinsic disorder, a large fraction of the electrons and holes are localized, but they can diffuse by following nearly adiabatically the evolution of the electrostatic potential. This process of diffusion, at a rate which is given by the lattice dynamics, contributes to the unique electronic properties of this material.