Probability of inflation

I've been reading this paper:
http://arxiv.org/PS_cache/hep-th/pdf/0410/0410270.pdf
and most of it makes sense, but there's one part I don't get.

Correct me if I'm wrong, but with temperature T, the odds against a
phenomenon with energy E randomly occurring at a given time where E T
are roughly exp(E/T), right?

On page 25 of the above paper, the authors consider a cold, empty
universe and the length of time it would take for a small region hot
enough to undergo inflation to spontaneously appear.

They come up with 10^56 as the difference between inflation temperature
and background temperature, which sounds reasonable. I therefore
expected the time estimate to be of the form exp(10^56), give or take a
factor of a few zillion.

The actual estimate given is of the form exp(exp(10^56)).

That number makes no sense to me; it's much larger than the number of
possible ways of arranging all the atoms in the visible universe. I
can't imagine any way any physical phenomenon under any set of physical
laws ever proposed could produce a finite number that large.
Unfortunately I don't know enough physics to follow the derivation given.

Can anyone explain in layman's terms where the triple exponential comes
from?

Thanks,

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