Let's say we have an ice water solution in an ambience with room temperature, i.e. there is a permanent exchange of energy. Let's suppose the ice cubes were from the freezer, which is at -18°C. The ice water has already reached its equilibrium at 0°. Now, through energy transfer into the system, the ice is melting. The energy is used up on the phase transition while the ice is melting.

(I'm also referring to the answers to [this question][1].)

The question is: Will the core temperature of the ice remain the same (-18°C) until it melts completely, as the energy it absprbs from the ambience is used up on the phase transition until there is no more solid water? Or will a temperature gradient form within the ice cube?
(For this question, the water isn't really needed; we can also suppose we just have an ice cube in a room temperature ambience.)


 [1]: http://chemistry.stackexchange.com/questions/5748/why-does-ice-water-get-colder-when-salt-is-added