The heat added to the solid is absorbed by the particles and it is utilised in overcoming the intermolecular force of attraction between the particles. So heat absorbed in solids is changed to potential energy without any change in kinetic energy of the molecules. As temperature in Kelvin scale is the measure of kinetic energy of particles, there is no change in temperature during melting.
If no heat is exchanged with surrounding, heat lost by the hot body is equal to heat gained by the cold body.
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