A radiative-thermal conduction model for the vertical thermal structure of Io's atmosphere is developed with solar heating by (\mathrm{SO}{2}) absorption in UV and near-IR bands and non-LTE cooling by (\mathrm{SO}{2} \nu_{1}, \nu_{2}, \nu_{3}), vibrational bands and rotational lines. The model predicts the existence of a mesopause in Io's atmosphere when the surface pressure exceeds (\sim 10) nbar. The radiative time constant for establishing a mesosphere/mesopause on Io is only (\sim 20 \mathrm{~min}), whereas the thermospheric radiative time constant is about (1 \mathrm{hr}). These time constants are significantly shorter than the diurnal time scale and competitive with dynamical time scales. In the thermosphere when solar UV heating dominates, the asymptotic thermospheric temperature is (\sim 270 \mathrm{~K}), only (140 \mathrm{~K}) greater than the surface temperature because at high altitudes non-LTE cooling by (\mathrm{SO}{2}) rotation lines exceeds cooling in the (\nu{2}) vibrational band. Solar-heating-only models are incapable of generating warm enough atmospheres to satisfy the observational inferences from UV and especially millimeter-wave measurements. Joule heating driven by the penetration of Jupiter's corotational electric field into Io's conducting ionosphere is demonstrated to be the dominant heating mechanism in the subnanobar regions of Io's atmosphere with temperatures ranging from 150 to (1000 \mathrm{~K}) as a function of decreasing pressure from 1 to 0.1 nbar. The asymptotic thermospheric temperature can attain a value as high as (1800 \mathrm{~K}). O 1994 Academic Press, Inc.