  We find exact finite temperature solutions to $d=5$ Einstein-dilaton gravity
with black branes and a Randall--Sundrum 3-brane. We show that there exists a
unique generating superpotential for these models. The location of the black
brane and the associated Hawking temperature depend on the value of the the
3-brane tension while other parameters are held fixed. The thermodynamics of
these solutions are presented, from which we show that the entropy satisfies
$S<\text{Vol}(\mathbb{R}^3)/4G_5$. We demonstrate that in a certain limit the
gauge dual of this theory effectively reduces to $\mathcal{N}=4$ SYM at finite
temperature on $S^1\times\mathbb{R}^3$
