The dirunal variation of the vertical structure of Titan's thermosphere is calculated through simultaneous solution of the equations of heat transfer and hydrostatic equilibrium. The temperature and density profiles are found above the mesopause. The dynamical response of the thermosphere to heating is for themost part neglected. Nevertheless, we are able to draw some interesting qualitative and quantitative conclusion regarding the vertical structure. Heating of the upper thermosphre occurs primarily through absorption of solar Lyman &agr; radiation by methane, with an additional amount of heating (≲20%) due to low-energy magnetospheric electron precipitation. The heat is conducted downward to the mesopause, where it is removed by IR cooling due principally to acetylene. The mesopause is found to occur where the density is 2.2¿1012 cm-3 (736 km) and has a temperature of ~110 K. The exospheric temperature is unlikely to exceed 225 K in the course of a Titan day. The diurnally averaged exospheric temperature is in the range 187--197 K depending on the amount of magnetospheric electron heating that is included in the model. The amplitude of the diurnal variation is found to be ≲28 K. We find that the vertical extent of the hydrogen cloud is too large to be explained in terms of simple thermal escape of hydrogen from a ~225-K exosphere, and we conclude that other processes must be important for populating or heating the neutral torus.