If there's no rain or snow falling from the sky and you're not in a cloud, the temperature decreases by about 5.4°F for every 1,000 feet (9.8°C per 1,000 meters) up you go in elevation.
If you’re in a cloud or if it's raining/snowing, the temperature decreases by about 3.3°F for every 1,000 feet (6°C per 1,000 meters) up you go in elevation.
You’re currently waiting to start your hike at the base of the mountain on a sunny but cold morning, with temperatures around 20°F. The summit elevation is 14,000 feet, while the base elevation sits at 11,000 feet.
This gives you 3,000 feet between the base and the summit of the mountain, bringing the temperature at the summit to about 16°F colder than at the base (3,000 feet elevation change at 5.4°F per 1,000 feet equals about 16°F temperature decrease). So the temperature at the summit should be around 4°F, withholding all other weather variables.
To recap, temperature changes 5.4°F/1,000 feet (9.8°C/1,000 meters) if it’s dry and 3.3°F/1,000 feet (6°C/1,000 meters) if it’s raining or snowing.
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