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I am thinking of digging a six feet narrow hole, and filling it in with a piece 2ft wide piece of sewage pipe, and using that as barrel style root cellar. The reason I want to go so deep, is that I am under the impression that the deeper it is, the cooler it will get.

Is this true? How much cooler can I make it?

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No, it is not true that necessarily the deeper you get the cooler it gets.

For really deep holes it is actually the opposite, the deeper you get the warmer the temperature gets. This is called the Geothermal Gradient. This states that temperature goes up 25C per 1KM of depth.

For the first couple of meters the temperature will likely drop or raise (depending on the above ground temp) dramatically. But it will then level off and begin to slightly increase. This is because your moving away from the influence of the Sun and start to be influenced by the temperature of the earth's core.

For a root cellar, you're not going to go 1km deep (obviously). You really need to think of a root cellar as a way to maintain (roughly) a constant temperature. The depth (that your likely to dig) alters this slightly but not much. This temperature could be hotter or colder than the temperature above ground, as shown in the picture below which are taken from http://www.builditsolar.com/Projects/Cooling/EarthTemperatures.htm.

Temperature over depth

This figure shows the maximum temperature deviation from the annual average is dampened out at about 30 feet depth. You can refer to the figure´s source for more detailed information, i.e. on seasonal changes.

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    I don´t think the geothermal gradient is of use here, as the surface has a lot more influence than this for depths below 10 meters. This site has a lot of great infos, especially figure 3 and 4 help a lot - you see that around 28 feet depth you have the locations average temperature constantly throughout the year. You don´t feel much of the geothermal gradient yet at this depth. – Paul Paulsen Jul 25 '14 at 14:44
  • That sites good @PaulPaulsen. I think were saying the same thing? I was more saying that technically it'll get warmer but at the depths were talking about this won't matter. – Liam Jul 25 '14 at 15:17
  • @liam I think the way you have it can be misleading as you put the emphasis on a not quite relevant fact. I don't think he's expecting to dig 1km; so why start with that fact? :) – ppl Jul 27 '14 at 17:34
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For any reasonable depth (ie. something you'd be willing to dig without specialized machinery), a deeper hole makes for a more stable temperature. The extra mass of soil surrounding your cellar acts to average out temperature changes: shallow burial averages out day-night shifts, while deeper averages out seasonal changes as well. The end result is that a deep enough hole will hold a constant temperature, at the annual average temperature of your location.

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    According to this website (almanac.com/root-cellar-build), completely stable temperature is reached at roughly 10 feet below the surface. In support of Mark's answer, when you analyze a root cellar as a heat transfer problem in engineering, you would use a "Semi-infinite body" model. An analysis of the model shows that the fluctuations in surface temperature (hot summer days, winter freezes, etc) have a much slower effect on your cellar's contents the deeper it is. Once you reach a depth at which the heat cannot reach within a single summer, there is no reason to dig deeper. – pheidlauf Jul 28 '14 at 13:41

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