To get rid of heat, you need to move the heat energy from the hot area to a cold sink. The heat energy the Earth is receiving is eventually radiated away to the cold and darkness of interstellar space, but since the Earth is an extremely complex and chaotic system (actually a series of systems like the atmosphere, the hydrosphere, the lithosphere and the ecosphere) there are no simple ways to map the various pathways heat energy arrives from the sun and departs.
What this really means is the heat energy in the ocean will only be temporarily diverted into melting the ice, but how it will affect the overall heat balance is not going to be predictable in any real or coherent way. A super volcano event like Tambora caused the "year without summer" by filling the upper atmosphere with aerosols, for example, but the resulting increase in smowcover or icepack did not start a global cooling chain reaction. Indeed, the only way we know for certain to cause such events as the "Little Ice Age" involve a reduction in the Sun's output, such as the Maunder Minimum between the 1400's and the late 1700's, or the current apparent reduction in solar activity which is happening now.
Warming periods are less predictable or explainable, the warm weather enjoyed by the Roman Empire or during the European Warm Period don't have an evident cause that we can point to, for example.
If the goal is to cool the Earth, the necessary thing to do is change the heat balance. Since the "cold sink" is already at an unvarying 3K, the place to interrupt the heat flow is to block the Sun with an orbital sunshade, perhaps at the Earth Sun L1 point or having millions of small mirrors orbiting the Earth (Injecting aerosols into the upper atmosphere, while known to work. would not be a quickly or easily removable as needed).
