As water depth increases, does temperature go below 0C?

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After passing the thermocline, in which water temperature decreases rapidly over short distances, temperature falls into a sort of constant-looking decline. However, looking at the graph, it looks almost asymptotic. I've not been able to find a chart measuring water depths below 10,000m, so I'm unable to tell for sure. What happens to water temperature as you dip to truly extreme depths, of which likely do not exist on Earth, like 10,000km? Would water temperatures ever reach absolute zero?
 
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The tendency for water to approach freezing as depth increases is an example of Le Chatelier's Principle. In the ocean, water is least dense at or just above freezing - depending on the depth. This link shows a chart: http://www.engineeringtoolbox.com/fluid-density-temperature-pressure-d_309.html

At pressures beyond what are found in the ocean, water tends to freeze - and form different kinds of ice. For example, at the normal boiling point (100C) but at pressure 30 times as great as the oceans get (10 GigaPascals), a type of ice forms called ice VII that is about 30% heavier than regular ice.

Other types of ice form at other pressures. This link describes them: https://en.wikipedia.org/wiki/Triple_point

https://en.wikipedia.org/wiki/Ice#Phases
 
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