Couze The water in the buket has some energy (tempreture) it is absorbed by the water and the ice melts this way water cools...now if you consider the ice outside the bucket water will no longer be in tuch with ice ,since energy of water since must be absorbed the ice first need to bring down the bucket's temp such that it must be less then the temp of water then the energy of water can be absorbed by the bucket and to the ice and surrounding (if its cooler)..

MORE GENRALY......

WITH OUT EXTERNAL AID TEMPERATURE FLOWS FROM HIGHER POTENTIAL TO LOWER POTENTIAL ALWAYS!

What's the question?

That's correct! Temperature, or thermal energy, always flows from a higher potential to a lower potential. In the scenario you provided, the water in the bucket has some energy (temperature) which is absorbed by the water itself and the ice. As a result, the ice melts and the water cools down.

If you consider the ice outside the bucket, the water will no longer be in direct contact with the ice. In order for the energy of the water to be absorbed by the ice, first, the bucket's temperature must be brought down to a temperature lower than that of the water. This is because temperature flows from higher potential (higher temperature) to lower potential (lower temperature).

So, without any external aid, the temperature will continue to flow naturally until it reaches equilibrium, where the temperatures of the water, ice, and surrounding (if it's cooler) are all the same. This is due to the principle that temperature always seeks balance by distributing heat energy from areas of higher potential to areas of lower potential.