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The air temperature in the sun and in the shade are actually the same temperature. The difference that you would measure with a thermometer in the sun and in the shade is not due to the surrounding air, but rather the radiation that the thermometer itself absorbs (transitioning into heat) and the heat that is radiated from surrounding structures and surfaces. But the temperature of the air itself is the same as air absorbs very little solar energy itself and is instead heated by heat from other objects like the Earth’s surface.

The Electronic Maximum-Minimum Temperature Sensor (MMTS) – an electronic temperature sensor that has largely replaced liquid-in-glass thermometers. It is housed in a white case to reflect sunlight and has vents all around so that the air flows freely over the temperature sensor inside. The idea is to measure the temperature in the shade, away from any direct effect of the sun.

What you are feeling when you step into the shade is a relief from the Sun’s photons and other forms of radiation (UV, infrared) that hit your skin and heat up your body. This is the sensation that makes it feel like the air is cooler.

This changes your body temperature in the absence of sunlight, but is not due (to the same extent) the surrounding air. [This is of course assuming that you are in a well-mixed environment like outside and step under a tree, and not into a freezer.]