Above the stratopause is a much cooler layer where the temperature again starts decreasing with increasing height. This layer is called the Mesosphere. It usually extends about 80 or 90 kilometres above the Earth’s surface.
At the top of this layer, we can encounter some of the coolest temperatures, as low as minus 180 degrees Celsius. You would find Noctilucent clouds in the upper Mesosphere, near the poles.
The upper boundary to the mesosphere is called the Mesopause, where the fall of temperature with height stops. The temperature remains constant at -90 to -100 degree centigrade.
Beyond the Mesosphere, you would find Thermosphere, in which temperature again rapidly increases with height. Temperatures in Thermosphere can reach up to 2000 degree centigrade. That is the reason for satellites burning out when they re-enter the atmosphere.
Finally, we have the Exosphere, which is beyond 700 KM of the earth’s surface. In this layer the air is totally rarefied, which can be said to be negligible.