The prodigious heat flux emitted from the surface of Jupiter's moon Io is produced in the interior of the satellite by viscoelastic dissipation of tidal energy and is generally thought to be brought to the surface by convective motions. New models of Io's equilibrium thermal state are constructed using self-consistent calculations of tidal heating and convective heat transport. These models show that while a high-temperature convective equilibrium exists, it falls an order of magnitude short of explaining the observed heat flux. Either Io is currently out of thermal equilibrium, or another heat transport mechanism such as melt segregation determines Io's thermal state.