The latent heat issue is indeed a big one. The total latent heat from melting$15,000$cubic km of ice (this$15,000$is an arbitrary number, but you could take it to mean a very large amount of melting) is$15000 \cdot 997\frac{\rm kg}{\rm m^3} $(the density of water)$ \cdot \, 334\frac{\rm kJ}{\rm kg}\,$(the enthalpy of fusion)$ \cdot \frac {1000 \, \rm J}{1 \, \rm kJ} \cdot \frac{10^9 \, \rm m^3}{1 \, \rm km^3}$=$4.995\times 10^{21}$Joules
Compare that to the total energy imbalance for the Earth of$0.58 \frac{\rm Watts}{\rm m^2}$(You can replace$0.58$with$1.17$if you think that is the real imbalance). For the whole surface area, thatcomes to$2.96 \times 10^{14}$Watts. Now, over a year, that energy imbalance is$2.96 \times 10^{14} \cdot \frac{365\, \rm days}{1\, \rm yr} \cdot \frac{24\, \rm hrs}{1\, \rm day} \cdot \frac{60\, \rm min}{1\, \rm hr} \cdot \frac{60\, \rm sec}{1\, \rm min}$. That's$9.33 \times 10^{21} J$.
So, one fair ratio of latent heat to energy imbalance is$4.995:9.33$. Of course, this assumes the$15,000$cubic km of ice is melted in one year. On the other hand, the relevant number for energy imbalance is also overestimated. That's because the amount of heat that is actually available to heat the earth is a tiny fraction of the imbalance (The exact fraction depends on the model you use). Regardless, latent heat is a major problem for further heating...scarily so.
