Earths core gains it’s heat from nuclear fission. There is also some frictional heat generation and heat left over from formation of the planet. But main point is that core is keeping itself hot.
Sea on the other hand don’t have internal heat source. It get’s it heat from either the sun or the planet core (underwater volcano). Now thanks to fact that hot water rises and loses heat in the surface and cold water falls down means that this current will always keep cold water down.
Third thing that makes sea bottom cold is fact that water is heaviest when it’s around 4 degree Celsius (or 40 Fahrenheit). This means that really cold water or ice will float preventing the bottom of the sea from freezing.
To recap. Three factors keep bottom of sea cold. They are lack of internal heat source, convection current and fact that coldest water is still liqued.
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