Amit compared amount of energy needed to melt a gram of ice to the amount of energy needed to heat a gram of water by 1°C.The values he uses for the amounts of required energy are right. The energy required to melt is
well-established in thermodynamics, and the energy needed to heat water by one degree is the definition of a calorie. The phase change energy needed really is that much bigger.
Now imagine what happens with climate change. If you add heat to a system, and there's ice around, it will melt the ice. But if there's no ice around, that same amount of heat will increase the temperature by 79.5°C (143°F).
Most of the talk about polar ice caps that I hear mentions its
reflective ability, which is important, and also mentions that they provide "cooling help". I've never seen the shocking magnitude of its cooling help discussed until that post.