In the absence of inversions, going up mountains will bring you into lower temperatures as you get higher.
What is the rule of thumb for how the temperature decreases with altitude?
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The answer is that it depends on the moisture held in the air
As moist air rises, it cools with height at a rate of 3°F per 1,000 feet (not nearly as fast as the dry-air rate of 5.4°F per 1,000 feet). Eventually clouds develop, and precipitation wrings moisture from the air. At the summit, the air is now both warmer and drier than air of the same altitude that has not climbed the mountain. But as the air passes over the summit and flows down the other side of the mountain, it compresses and warms at 5.4°F per 1,000 feet (now following the dry-air rate), creating a much warmer, dryer wind.
In Freedom of the Hills , they use an estimate of 3.5° Farenheit /2 ° Celsius per thousand feet to estimate the freezing level.
The idea is that if you know your elevation, the elevation you are going to and the temperature where you are, then you can use those pieces of information to estimate the temperature at the elevation you are headed to.
For instance, if base camp is at 11,000 ft and the peak is at 13,000 ft, then it will be approximately 7° Farenheit / 4° Celsius colder at the peak. This could be useful for calculating whether the snow will be frozen on the way up.