Does an ice cube change its core temperature as it melts?

$ \begingroup $ Let ‘s say we have an internal-combustion engine body of water solution in an atmosphere with room temperature, i.e. there is a permanent exchange of energy. Let ‘s suppose the frosting cubes were from the deep-freeze, which is at $ -18°C $. The ice rink water has already reached its chemical equilibrium at $ 0° $. now, through energy transfer into the system, the ice is melting. The energy is used up on the phase passage while the ice is melting .
( I ‘m besides referring to the answers to the wonder Why does ice rink water get cold when salt is added ? )
The question is : Will the core temperature of the ice remain the same ( $ -18°C $ ) until it melts completely, as the energy it absorbs from the ambiance is used up on the phase transition until there is no more solid water system ? Or will a temperature gradient human body within the ice cube ? ( For this question, the water is n’t in truth needed ; we can besides suppose we fair have an ice cube in a room temperature ambiance. )

EDIT for disambiguation : I ‘m perfectly mindful that a body that absorbs energy will radiate the energy by forming a gradient from its center to the outside that is the connecting point to the atmosphere it exchanges energy with. But : When a mass is undergo phase transition, all invested energy ( or radiated energy, depending on the focus it is going ) will be used up on the phase transition. E.g., when you cool water below $ 0°C $, it will not get cold ( let ‘s leave out supercooled water here ) until it has frozen wholly ( frankincense the ice water equilibrium ). same happens when you heat water that has a temperature of $ 100°C $. It will not get warmer unless all has evaporated.

now we have our methamphetamine cube with $ -18°C $ in its core. We heat it. On its surface, a dynamic chemical equilibrium of freeze and dissolve is formed, with more water melting than freezing. The body of water always has a temperature of $ 0°C $. now if we add some more department of energy to the cube, will the extra energy lend completely to the phase passage, resulting in less freeze and frankincense more mellow in the active equilibrium – or will some of the energy contribute to heating the methamphetamine cube itself ? If thus, why is not all the energy used on the phase transition, and how much is not used on the phase transition ? For a thorough answer, I feel that it is this point that has to be answered .
Of course, size matters here. directly adjacent to the come on, a small gradient may take place ; and when the come on gets closer to the core, at some point, it will affect it anyhow. But – and that ‘s the big but here : According to the above mentioned phase conversion energy absorption, you could argue that it will differ a lot from a temperature gradient in a solid body, because of the energy “ drained ” by the phase transition .
note to the moderators : Feel unblock to move the question to chemistry.SE if you think that it better fits there ; many questions on the ice-water-salt-topic have already been asked in chemistry.SE, but I posted it here as I felt that general thermodynamics contribute more to the whole ice-water-system than chemical processes ; but then again, rethinking it, it ‘s hard to tell !