The Earth's ice caps were completely melted from:
-The early Ediacaran period (about 620 million years ago) to the late Ordovician (about 445 million years ago),
-The early Silurian period (about 444 million years ago) through the Devonian period (about 350 million years ago)
-The early Triassic period (240 million years ago) through the early Miocene epoch (until about 15 million years ago)

It is very unlikely that the Earth's southern hemisphere (Antarctic) ice cap will melt for the foreseeable future. The Greenland ice cap may melt, though.

There is argument over what the pattern is. One observation is that ice caps form when continents occur over poles, especially symmetrical continents (Antarctica is roughly circular). There also seems to be a correlation between carbon dioxide levels and global ice volume, but telling cause from effect is difficult, because carbon dioxide is more soluble in cold water, so cooling the Earth's oceans would have the effect of removing carbon dioxide just as adding carbon dioxide would increase temperature due to the greenhouse effect.