Question: We often seem to accept the idea that there were periods of time in which the entire surface of Earth was frozen, for the most part. This implies that there were periods of time in which the entire surface was NOT frozen over. Thus, there must have been heat and energy present on the surface. How did all that energy move to cause an ice age? It seems absurd for all that energy to just radiate into space or move deep into the Earth.

Answer: 
Of course it isn't "absurd", and looking at the ball-park energy budget figures you'll see why:

First, I don't think anyone is claiming the Earth is completely frozen. More of a "slushy at the Equator" scenario. But let's assume an average 1 km thickness of ice for arguments sake (i.e. probably an exaggeration although polar ice would be thicker).

The current thermal budget [can be found here](http://en.wikipedia.org/wiki/Earth%27s_energy_budget%20including%20references.).

Pertinent figures:

Geothermal heat flow (vertically through the rock, primarily from radioactive decay & cooling) is ~$0.084\ \mathrm{W/m^2}$.

Solar input: $340 \mathrm{W/m^2}$ About a quarter of this is reflected back but this will vary according to conditions (e.g. ice cover, clouds, etc). Assume no reflection. (yes the presence of ice would cause reflection - but it may also reduce cloud cover due to reduced evaporation?).

Note: geothermal energy is tiny relative to solar flux, so we'll ignore it.

That 1 km of ice = 1000m3 of ice (per square meter).

Let's assume that the melting process would also involve an increase in 10C in additional to the latent heat of melting (ie. yes we melt the water but we also increase its temperature a bit).

Total energy required (per $\mathrm{m^3}$) = (Temp increase \times Thermal capacity of water + Latent heat of melting) × volume.

So if we plug in our numbers, that would be:

$$(10 \times 4.2 + 334) \times 10^6 \times 1000$$
$$= 3.8 \times 10^{11}\ \mathrm{Joules}$$

Heat flux for the same area is $340\ \mathrm{J/s}$
So time for the required energy to melt the ice = $3.8 \times 10^{11} / 340 = 35\ \mathrm{years}$.

You could argue about my ball-park estimates. For example there would be more albedo reflection to melt the ice (=takes longer). And you may not necessarily have to increase the temperature of the water as much ( =>takes less time), and much of the Earth would not have 1 km of ice (=>takes less time). But this gives you a ball park "yes it is feasible".

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Edit: I read the question a bit quickly - the above shows it is 'easy' to get from an ice planet to an ice-free planet. But the converse is also true. The amount of energy that keeps the Earth ice free can easily be added/subtracted over a timescale of a few centuries, just from solar and atmospheric effects.
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 I propose that the “snow ball Earth” was brought to a close by the dust from a huge meteorite (the largest known on Earth) impacting Australia (see <http://charles_w.tripod.com/antipode.html> ) settling onto the ice and melting it by a bare soil warming affect (see <http://charles_w.tripod.com/climate.html> ) and thus initiating the Cambrian. The dust fertilizing the ocean probably contributed considerably to the explosion of life then. That initiation was probably considerably assisted by the subsequent release of methane gas from methane ice under the ocean floor and by dust from volcanic eruptions from the Bahamas Islands, which are located at the antipode (opposite side of a sphere) of the above impact. The close correlation of volcanoes on Mars with meteorite impacts at their antipodes gives supporting evidence for such a phenomenon. 

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 Sincerely, Charles Weber