Venus has thick clouds of H2SO4 aerosol particles extending from altitudes of 40 to 60km. The 60-100km region (the mesosphere) is a transition region between the 4day retrograde superrotation at the top of the thick clouds and the solar-antisolar circulation in the thermosphere (above 100km), which has upwelling over the subsolar point and transport to the nightside. The mesosphere has a light haze of variable optical thickness, with CO, SO2, HCl, HF, H2O and HDO as the most important minor gaseous constituents, but the vertical distribution of the haze and molecules is poorly known because previous descent probes began their measurements at or below 60km. Here we report the detection of an extensive layer of warm air at altitudes 90-120km on the night side that we interpret as the result of adiabatic heating during air subsidence. Such a strong temperature inversion was not expected, because the night side of Venus was otherwise so cold that it was named the `cryosphere' above 100km. We also measured the mesospheric distributions of HF, HCl, H2O and HDO. HCl is less abundant than reported 40years ago. HDO/H2O is enhanced by a factor of ~2.5 with respect to the lower atmosphere, and there is a general depletion of H2O around 80-90km for which we have no explanation.