We study the finite-temperature properties of the Randall-Sundrum model in the presence of brane-localized curvature. At high temperature, as dictated by AdS/CFT, the theory is in a confined phase dual to the planar AdS black hole. When the radion is stabilized, à la Goldberger-Wise, a holographic first-order phase transition proceeds. The brane-localized curvature contributes to the radion kinetic energy, substantially decreasing the critical bubble energy. Contrary to previous results, the phase transition completes at much larger values of N , the number of degrees of freedom in the CFT. Moreover, the field value of the bulk scalar on the TeV-brane is allowed to become large, while remaining consistent with back-reaction constraints. Ass...