Venus and Earth have similar radii and estimated bulk compositions, and both have an iron core that is at least partially liquid. However, despite these similarities, Venus lacks an appreciable dipolar magnetic field. Here I examine the hypothesis that this absence is due to Venus's also lacking plate tectonics for the past 0.5 b.y. The generation of a global magnetic field requires core convection, which in turn requires extraction of heat from the core into the overlying mantle. Plate tectonics cools Earth's mantle; on the basis of elastic thickness estimates and convection models, it is argued here that the mantle temperature on Venus is currently increasing. This heating will reduce the heat flux out of the core to zero over ̃1 b.y., halting core convection and magnetic field generation. If plate tectonics was operating on Venus prior to ca. 0.5 Ga, a magnetic field may also have existed. On Earth, the geodynamo may be a consequence of plate tectonics; this connection between near-surface processes and core magnetism may also be relevant to the generation of magnetic fields on Mars, Mercury, and Ganymede.