  We analyze the thermodynamical properties of brane-worlds, with a focus on
the second model of Randall and Sundrum. We point out that during an
inflationary phase on the brane, black holes will tend to be thermally
nucleated in the bulk. This leads us to ask the question: Can the black hole -
brane-world system evolve towards a configuration of thermal equilibrium? To
answer this, we generalize the second Randall-Sundrum scenario to allow for
non-static bulk regions on each side of the brane-world. Explicitly, we take
the bulk to be a {\it Vaidya-AdS} metric, which describes the gravitational
collapse of a spherically symmetric null dust fluid in Anti-de Sitter
spacetime. Using the background subtraction technique to calculate the
Euclidean action, we argue that at late times a sufficiently large black hole
will relax to a point of thermal equilibrium with the brane-world environment.
These results have interesting implications for early-universe cosmology.
