Motivated by recent experiments, we explore the kinetics of Bose-Einstein condensation in the upper band of a double-well optical lattice. These experiments engineer a nonequilibrium situation in which the highest energy state in the band is macroscopically occupied. The system subsequently relaxes and the condensate moves to the lowest energy state. We model this process, finding that the kinetics occurs in three phases: The condensate first evaporates, forming a highly nonequilibrium gas with no phase coherence; energy is then redistributed among the noncondensed atoms; finally, the atoms recondense. We calculate the timescales for each of these phases and explain how this scenario can be verified through future experiments. © 2020 American Physical Society.