Although the stratospheric temperature inversion is clearly due to absorption of sunlight (and terrestrial emission in the infrared), it is not established that fluctuations in ozone are responsible for fluctuations in stratospheric temperatures. A large data base of radiosonde temperatures is available, but the only comparable data for ozone are the total column densities. We find that fluctuations in total ozone and radiosonde temperatures in the lower stratosphere (50-100 mbar) show correlations of the magnitude expected for ozone control of the heating. At the higher altitudes examined in this study (10-30 mbar) the relationship between ozone and temperature is diminished, possibly because of (1) overhead changes in opacity with a change in the local ozone concentration (negative feedback), (2) dependence of the local ozone concentration on temperature (which offsets the dependence of T on 3>), and (3) adiabatic dependences of T on density arising from the vertical components of ozone transport (which are not necessarily dependent on ozone absorption). At low altitudes, just above the tropopause in the sub-tropical summer, the heating of the stratosphere is due mainly to absorption of ground radiation in the 9.6μm O3 band and direct solar radiation in the near ultraviolet, and the confusing factors that occur at higher levels and high altitudes are diminished.