Ice in the refrigerator.

Now if a block of ice, was kept in the chiller compartment of a refrigerator, what would happen to it ?

would it melt ? because according to the thermodynamic laws, there would be heat exchange between hot and colder bodies, and since the temperature of the ice would be lower than that of the other things placed in the compartment.

Besides the temperature in the chiller would not be that low enough to freeze water.

what do you feel about it ?