A three-dimensional simulation of the deflagration-to-detonation transition (DDT) in a H-2/O-2 mixture in a rectangular tube is performed under adiabatic and isothermal wall boundary conditions. In the isothermal wall boundary case, a local explosion triggering the onset of detonation occurs near the center of the tube behind the incident shock wave, which agrees qualitatively with the two-dimensional simulation in our earlier study. In contrast, in the adiabatic case, auto-ignition is observed near the corner of the tube before the local explosion occurs on each wall behind the flame, which is accelerated by the high-temperature condition (preheated zone) caused by the generation of compression waves. The flame overtakes the incident shock and propagates toward the upper and lower walls. In some experimental studies, the local explosion occurred near the wall. Therefore, the present adiabatic case received special attention. Moreover, these phenomena are discussed in detail in terms of the flame acceleration, preheated zone, and x-t diagram.