Final answer:
The stratosphere and the thermosphere are the atmospheric layers where temperature generally increases with altitude, due to the absorption of UV radiation by ozone in the stratosphere and high-energy solar radiation in the thermosphere.
Step-by-step explanation:
The layers of Earth's atmosphere that mostly observe an increase in temperature with altitude are the stratosphere and the thermosphere.
In the stratosphere, which extends from about 10 kilometers to about 50 kilometers above Earth's surface, temperature rises due to the absorption of ultraviolet (UV) radiation by the ozone layer. The thermosphere, starting just above the mesosphere at around 85 kilometers and extending to 600 kilometers, sees a significant increase in temperature as altitude increases. This is partly because it directly absorbs a vast amount of high-energy solar radiation.
At the boundary between these layers, such as the thermopause, temperatures can soar to 2000 degrees Celsius or more. However, because the air is so thin at these altitudes, it would not feel warm to the touch.