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If the daily air temperature is between 0 °C to 14 °C, what sort of temperature would be found within caves? Will it be any colder or warmer? The caves in question (Wombeyan) do not go terribly far underground.

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The temperature within the cave is almost constant whatever the current surface temperature is.

Once well away from surface influences, i.e., not near an entrance or another close connection to the surface, where air movements can influence the temperature, caves are usually at the same temperature (or very close) as the annual average temperature for the cave's location all year round.

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    It gets warmer as you go deeper down. – gerrit Jun 4 '14 at 14:40
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    The only place underground I have experienced warmer temperatures at depth was in a Potash mine which was 1,400 metres (4,600 ft) deep. At that depth the temperature was 45 C/113 F. But that was because of local geology, not because of the depth (1,400 metres is extremely small in relation to the thickness of the earth's crust). Krubera Cave (also known as Voronya Cave), in Abkhazia, Georgia is the deepest known cave in the world at present at over 2000 metres/6561 feet but the cave is very cold, with temperatures of 1.0 C at 100 metres depth, rising slowly up to 7.2 C at 2000 m depth. – Paul Lydon Jun 4 '14 at 17:31
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    I disagree. At most places temperatur rises about 25-30 Kelvin per km depth (3 K per 100m), which is also according to my personal experiences. At tectonic active locations this is likely to be higher. However, mines have air conditioning (not sure if this is the right word) supplying fresh air. Not sure about resons for Krubera Cave being so cold. General info at wikipedia. – Paul Paulsen Jun 4 '14 at 21:15
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    We can agree to disagree on the rate at which temperature increases with depth. However, the point is that for a given depth underground, the temperature is fairly constant irrespective of changes at the surface and for the majority of caves, which are not that deep after all, it will be pretty near to the local average temperature give or take a few degrees. This is more in line with the original question. – Paul Lydon Jun 5 '14 at 9:06

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