The sun heats the earth and the earth re-radiates some of that heat into cold space. How much it radiates is a function of its temperature. Heat always moves from hot to cold. When it reaches the poles it melts ice. It takes latent heat, heat that does not raise the temperature, to melt ice. When ice melts and temperature stays the same the amount of heat re-radiated into space remains the same. So the imbalance remains. If all the extra heat was latent heat, the earth would continue to absorb extra heat until all the ice was gone. This would be true even if the incoming-outgoing imbalance were small. Only an increase in the earth's temperature can restore the balance.
Total melting doesn't happen with small imbalances because of the inefficiencies in the transfer of heat to the poles. Much of the extra heat does raise the temperature and never gets to the poles simply because of the inefficiency of winds and currents. Re-radiation increases. The deformation of the jet stream and the disruption of currents will, given the second law of thermodynamics, tend to reduce these inefficiencies. So, paradoxically, since there is an imbalance, no global warming, where all the heat goes into melting ice, is worse than global warming, because it won't stop until all the ice is gone.