Converting water into ice is a two-stage process. The first involves normal refrigeration to cool the water to 0°C; the second converting the water at 0°C to ice at 0°C, which uses many times more energy than the cooling process. This extra energy is locked into the ice until it starts to melt. When the melt starts, the ice releases some of this energy to lower the temperature, and it tends to re-freeze some of the melt water, forming a skin and further insulating itself.
Since ice is a good insulator, the cycle can continue for quite a time. In a fishing boat hold, the excess water drains off and keeps any draft away from the ice, so the fish gradually coats itself in ice and the temperature remains stable.