With this theory, the reversal can be attributed to the movement of the hot spots in the earth's core. An explanation for the large variations in the cycle time of ice ages before the previous ten is that the movement of tectonic plates could cause oceans to heat differently, or the movement of hot spots in the earth could be variable. During the sixties, the common theory was that ocean levels increase and decrease in a cyclic manner. As the oceans rise, they melt the polar ice caps causing another ice age. This theory also seems to suggest increased rainfall at the beginning of ice ages.
Atmospheric temperature has little relevance to anything.
The main reason is because there is very little heat capacity to air. When snow melts in the spring, air temperature has very little effect, while radiation does most of the melting. On a cloudy day, little snow melts, even when air is warm, because air has very low heat capacity. What this means is that ice accumulates during ice ages not because the air gets cold but because overcast skies block out the sun's radiation. The best explanation I can imagine is the oceans heating up.