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Good thinking! Ice melts at $$0^{\circ}\mathrm{C}$$. Which means that ice can never reach any temperature more than $$0^{\circ}\mathrm{C}$$, because it would have turned into water by then.
The heat that is absorbed by a solid at its melting point is called latent heat of fusion. Fusion is just a fancy word for melting!

Normally, on heating an object, its temperature increases. But, if the object is at its melting point, all the heat is used up in changing its state from a solid to a liquid.