Real snow doesn’t appear overnight in sheets hundreds of metres deep. Instead it builds up slowly in layers.
And so in the next, slightly more realistic model, snow is dropped at a constant steady rate to form layers of snow.
Once again, as snow depth builds up, subglacial surface rock temperatures rise. At first the rate of melting of the snow at the base of the ice sheet is less than the rate at which snow is added on the surface of the ice sheet, and the ice deepens. But as the surface rock temperature rises, the rate of snow melting increases until it equals – and then exceeds – the rate of surface snow deposition. The snow sheet first gets deeper, and then gets shallower, even though snow falls at a constant rate.
But after a while the snow sheep gets no shallower. This because, as the snow sheet thins, its thermal resistance falls, and heat flow out of the snow sheet increases until it equals the heat flow from the rocks beneath. When heat flow in equals heat flow out, the snow sheet stops melting.
Even when the snow stops falling after 100,000 years, and most of it melts, there still remains a thin layer of snow.
If thin layers of snow don’t melt, how then did the ice age end?