A 1-1/2-D tokamak transport code is used to model the evolution of doublet geometry on the transport time scale. The doublet shape is determined by the plasma current profile and the current flowing in the field-shaping coils. The current profile is determined in turn by the assumed transport mechanisms for the densities and temperatures and by any auxiliary heating which may be present. In a large hot machine, such as Doublet III, the time-dependent current profile will also depend upon the assumed initial profile because the skin time is long. As the plasma current evolves, the field-shaping coils must be actively programmed to preserve a desired shape. Using an idealized transport model and a DIII-size plasma, the effects of these key elements upon shape evolution are illustrated, and control of doublet equilibria on a transport time scale is demonstrated for this model. The components of the current profile (p' and ff') obtained should serve as a guide to selecting realistic profiles for MHD stability studies.