Even if assuming no heat was emitted form the Earth (and as no significant part of the sea bed is below the freezing point of water this is not a valid assumption, even as an approximation), then the ice has to float its way to the bottom, sometimes several miles, without warming enough to melt. Considering that it would start to sink the instant it froze, then theoretically, it would instaneously meet water warmer than itself and instantaneously reliquify.
Another way to look at it is as follows: there is a certain amount of thermal energy in the entire ocean. It is receiving energy from its warmer surroundings and from radiation and it is losing heat to its cooler surroundings and by giving off a smaller amount of radiation. Whether ice or water is more dense makes little difference to the rate of loss or gain of the thermal energy.
And one other thing that springs to mind: Warm air rises and air at ground level is more dense than air 10 miles up. But the air at ground level doesn't get cooled to the temp. of the air ten miles up by freezing downdrafts. The same would apply for a significant volume and head of water.
