Given that the scattering of sunlight by the Earth's atmosphere above 30-35 km is primarily due to molecular Rayleigh scattering, the intensity of scattered photons can be assumed to be directly proportional to the atmospheric density. From the measured relative density profile it is possible to retrieve an absolute temperature profile by assuming local hydrostatic equilibrium, the perfect gas law, and an a priori temperature from a climatological model at the top of the atmosphere. This technique has been applied to Rayleigh lidar observations for over 35 years. The GOMOS star oc-cultation spectrometer includes spectral channels used to observe daytime limb scattered sunlight along the line of sight to a reference star. GOMOS Rayleigh scattering profiles in the spectral range of 420-480 nm have been used to retrieve temperature profiles between 35 and 85 km with a 2 km vertical resolution. Using this technique, a database of more than 309 000 temperature profiles has been created from GOMOS measurements. A global climatology was constructed using the new GOMOS database and is compared to an external model. In the upper stratosphere, the external model is based on the ECMWF reanalysis and the agreement with GOMOS is better than 2 K. In the mesosphere the external model follows the MSIS climatology and 5 to 10 K differences are observed with respect to the GOMOS temperature profiles. Comparisons to night-time collocated Rayleigh lidar profiles above the south of France show some vertical structured temperature differences, which may be partially explained by the contributions of the thermal diurnal tide. The equatorial temperature series shows clear examples of mesospheric inversion layers in the temperature profiles. The inversion layers have global longitudinal extension and temporal evolution, descending from 80 to 70 km over the course of a month. The climatology shows a semi-annual temperature variation in the upper stratosphere, a stratopause altitude varying between 47 and 54 km, and an annual variation in the temperatures of the mesosphere. The technique that derive temperature profiles from Rayleigh limb scattering can be applied to any other limb-scatter sounder, providing that the observations are in the spectral range 350-500 nm. Due to the simplicity of the principles involved, this technique is also a good candidate for a future missions where constellations of small satellites are deployed.