We investigate the transport properties of itinerant electrons interacting with a background of localized spins in a correlated paramagnetic phase of the pyrochlore lattice. We find a residual resistivity at zero temperature due to the scattering of electrons by the static dipolar spin-spin correlation that characterizes the metallic Coulomb phase. As temperature increases, thermally excited topological defects, also known as magnetic monopoles, reduce the spin correlation, hence suppressing electron scattering. Combined with the usual scattering processes in metals at higher temperatures, this mechanism yields a nonmonotonic resistivity, displaying a minimum at temperature scales associated with the magnetic monopole excitation energy. Our calculations agree quantitatively with resistivity measurements in Nd2Ir 2O7 and Pr2Ir2O7, shedding light on the origin of the resistivity minimum observed in metallic spin-ice compounds.