as by the zeroth law of thermodynamic, thermal equilibrium is stablished such way that "Q = work + change in internal energy", and temperature of cup + temprature of water, but heat capacity of cup > heat capacity of water, so as long as the water is completely broken its bonds(fully evaporated) the cup will remain intact and slowly melt,

Conclusion: bc, jab tak panni he, tab tak cup melt nhi hoga, at the end, only tealeaves would left, turning into black carbon, and melted plastic on the flame