Transient three-dimensional mixed convection of air in a differentially heated vertical cubic cavity rotating about a vertical axis through the cavity center is numerically investigated. The unsteady Navier-Stokes and energy equations were discretized by the power-law scheme and solved by the projection method. Results were obtained for the thermal and rotational Rayleigh and Taylor numbers all varied from 10(2) to 10(7). Effects of the centrifugal and Coriolis forces on the thermal buoyancy driven flow were examined in detail. Significant flow modification was noted when Ra-omega > Ra or Ta > Ra. It was noted in a rotational buoyancy dominated flow that after the initial transient the main flow structure is characterized by a symmetric pair of longitudinal rolls with their axes parallel with the rotating axis of the cavity. The increase in the Coriolis force decelerates the flow near the walls and reduces the heat transfer. The local Nusselt number distributions on the hot and cold plates were more sensitive to the change in the driving forces than the space average Nusselt numbers.