That's how it starts, sure.

Give that state you described another 50 odd years again and things can get worse - the land based glaciers are already greatly reduced, almost gone. The bulky polar ice is retreating a little - but the warming sea surface is the thing, it'll carry warm water and melt more and more ice.

Now it's fun and games for predicting what comes next - the insulation in the atmosphere is still increasing and the same amount of trapped energy that now goes to turning a mass of ice to a mass of water (at much the same temperature) will now turn to raising that same mass of water from near 0 C to about 60 C (roughly IIRC) - speeding up ice melts.

There's also the increasing amounts of water and methane in the atmosphere that come along with rising temperatures, these are much much better insulators that measly old CO2 and will serve to trap ever more energy from the sun.

Geophysically that's how this all goes in the absence of any serious reduction of insulation in the atmosphere.