Step 1: Concept
During a change of phase (melting or boiling), the temperature remains constant while heat is absorbed (Latent Heat).
Step 2: Meaning
The heating curve will show horizontal segments at $0^{\circ}C$ (melting) and $100^{\circ}C$ (boiling).
Step 3: Analysis
Graph A represents the melting of ice at $0^{\circ}C$ (first plateau), the warming of water to $100^{\circ}C$ (sloping line), and the boiling of water at $100^{\circ}C$ (second plateau).
Step 4: Conclusion
Hence, option A is the correct representative curve.
Final Answer: (A)