The mesopause is the coldest level of the atmosphere, the lower mesosphere is warm.
In the thermosphere, the molecules of gas in the outer atmosphere are few and far between and so are free to move. Temperature is a measurement of the motion of the molecules, the more they move the higher the temperature. As you descend through the thermosphere, the air becomes denser and the molecules are closer together. The thermosphere also absorbs solar radiation such as xrays which warms the layer. This activity is at a minimum just above and down to the mesopause.
Through the mesosphere the temperature rises as the action of UV radiation causes oxygen molecules to combine with free atoms of oxygen to form ozone. The heavier ozone sinks into the stratosphere where it is broken up into oxygen moleclues and atoms again, The free atoms rise into the mesosphere and the process starts again. The absorption of UV radiation in this process reaches a peak at the stratopause which is, consequently, warm.
The temperature falls through the stratosphere to reach a low at the tropopause and then the temperature rises through the troposphere as the air is heated by the ground below.
The coldest part of the atmosphere is, therefore, the mesopause with the tropopause being the second low temperature point.
Hope this helps:)