The ice has been melting since the last ice age. Are you aware the glaciers were as far south as NYC just 20,000 years ago? The glaciers had already melt back thousand of miles, before some humans tried to take full credit.
Today about 10% of the earth's landmass is covered by glaciers and the oceans are 400 feet higher. You guys are seeing melting but your primary cause explanation is more political science than earth science. That is an artifact of black box science and not rational science.
Water vapor has more than double the heat capacity of the two main gases in the atmosphere; nitrogen and oxygen. Carbon dioxide gas also has about half the heat capacity of water vapor. There is about 4% water vapor in the atmosphere, today. If we treat the atmosphere as an average, the 4% water in the atmosphere acts like 8% in terms of the total atmospheric heat capacity. As the water vapor content increase, due to warming, waters's heat capacity contribution increases more than by a linear relationship; see graph below. During an ice age, the cold air holds less water vapor making the entire atmosphere cool faster.
Below is the moisture carrying capacity of air as a function of temperature. One can notice how the slope is not linear but rather the slope increases with increasing temperature. The glacial ice can create an ice cooler buffer in terms of any temperature increase by keeping the water contribution, lower in the atmosphere; less total air heat capacity. Water vapor limitations in air is why the glacier melt is not as fast as originally thought. When the glacier started to melt 20,000 years ago, the ice box effect made the first melting much slower, with the rate rising with atmospheric temperature due to water's double heat capacity and more water in air as water content versus temperatures increase faster than just a linear relationship.
Water is also interesting in that liquid water expands when it freezes. Liquid water has a maximum density at 4C ,and will expand from there whether you heat it or cool it. Water is weird that way. Nearly all other liquids get denser as they cool and then become solid. If water was just another liquid, the cold air of the winter would freeze the Oceans over time. But the anomalous expansion behavior of water and ice prevents this.
As water gets colder heading toward 4C, it gets denser and sinks in the warmer water, with the warmer water rising. At 3C, since water get less dense and is now lighter than at 4C, the colder 3C water will float on the 4C water. The extra cold does not make it downward by normal convection, but can by radiation, which is slower and less effective. And as the ice forms and gets thicker, it will float no matter how cold it gets, with 90% below the surface. The density maximum at 4C and the expansion of ice seals the ocean from getting too cold. The ice build up as glaciers and not down as a frozen ocean.
On the other hand, heat also comes into the oceans from the ocean floor; heat vents and crustal boundaries. The heat capacity curve for liquid water is also different. It is more like a bowl shape with a minimum at 40C. As the hot vent water rises and cools, and the cool ocean water warms, via the vent, the total combined heat capacity lowers toward the minimum; 10C water heads toward 40C and 90C waterheads toward 40C. We get a beach sand effect that makes the water get warmer; temperature, than expected, if we assume a linear heat capacity curve.