mesosphere

That region of the atmosphere which lies above the stratopause (about 4752 km) and below the mesopause (about 8090 km) and in which temperature decreases with increasing height; this is the region in which the lowest temperatures of the atmosphere occur.
Source:
PAC, 1990, 62, 2167 (Glossary of atmospheric chemistry terms (Recommendations 1990)) on page 2201