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In matters of height i will assume you are talking about a rather size-able mountain, along the lines of something like Mt. Rainier In Washington state. or Mt. Saint Hellens ( before she blew her top )

The reason the top of a mountain is colder than the bottom is quite simple. The air you breathe is called Atmosphere the closer to the surface of the earth the denser the Atmosphere. As you ascend a mountain, or gain altitude the Atmospheric Pressure reduces.

This reduction in the density of the atmosphere does not allow for the storage of the same amount of heat as lower altitudes. There are many layers of atmosphere, and some Mountains can penetrate several of them.

I have included a link to an image pulled from Google image search to further illustrate. See Related Link

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