Water vapour is a potent greenhouse gas, and the observed increases in water vapour in the stratosphere act to cool it. Possible changes in stratospheric temperatures are important for future ozone loss because colder temperatures in the edge region of the Antarctic ozone hole act to increase polar stratospheric clouds there, and so delay recovery of the ozone hole. Trends in lower-stratospheric temperature within the core of the Antarctic vortex in winter should be a unique indicator of trends in stratospheric water vapour, because neither changes in CO2 nor in ozone have a large effect on temperature in the lower stratosphere in the dark. Here, measured stratospheric temperatures southward of 70 S in winter are presented and their quality and corrections discussed. The character and magnitude of the long-term changes at Halley (76 S) are similar from 100 to 70 hPa and at 50 hPa, whether corrected for sonde changes or not, and are also similar to those at other Antarctic sites. We found no significant trend in temperatures at Halley between 1960 and 2000, which is inconsistent with the change calculated from the trend in lower-stratospheric water vapour in northern hemisphere midlatitudes between 1960 and 2000. Over the shorter interval between 1980 and 2000 at Halley, the change in temperature was -1.8 +/- 0.6 K, in agreement with the change calculated from the trend in stratospheric water vapour in northern hemisphere midlatitudes between 1980 and 2000. The differences between these periods are discussed in terms of: possible fortuitous agreement between 1980 and 2000; the poorer representation and quality of the measurements of stratospheric water vapour between 1960 and 1980; and a possible large variation in the rate of oxidation of CH4 to H2O in the upper stratosphere between 1960 and 1980. Such a variation in oxidation rate was observed by satellite between 1992 and 1999.