The atmospheric structure of Triton in the altitude range 25-150 km shows an unexpectedly steep thermal gradient of 0.26 K km -1 above 50 km altitude, with a nearly isothermal profile below. The upper part of the profile can be explained by downward conduction of heat deposited by magnetospheric electrons and solar UV. However, the atmospheric temperature below 50 km is too cold for identified radiative processes to dispose of the inferred heat flux (0.0012 erg cm -2 s -1) from the upper atmosphere. This implies that either the atmosphere is not in a steady state and/or an unidentified cooling mechanism is at work in the altitude range 25-50 km. When extrapolated to the surface, the inversion results yield a pressure of 19.0 -1.5+1.8 μbar, about 5 μbar greater than that observed by Voyager.