More than 500 nightly mean temperature profiles have been obtained since 1981 by two Rayleigh lidars located in south of France 550 km apart. In the mesosphere a temperature inversion, a feature persisting for several days, is frequently observed simultaneously at both sites. From a statistical study of the inversion characteristics, it is shown that its altitude ranges from 55-72 km in winter to 70-83 km in summer, while its probability of occurrence presents a semi-annual variation with a maximum higher in winter than in summer and a minimum lower in May than in September. The seasonal variation of the temperature inversion is shown to be very similar to that of the MST radar echoes in the mesosphere associated to turbulent layers generated by the breaking of gravity waves. A crude estimate of the amplitude growth with height of a gravity wave in the presence of an inversion layer indicates that the wave will break preferably inside and above this layer. The persistence of a temperature inversion during several days, with amplitude as large as 40 K, is tentatively explained by the heating of the turbulent layers generated by the continuous breaking of gravity waves above the secondary minimum of temperature.