The transient motion and heat transfer of a viscous incompressible fluid contained between two concentric spheres, maintained at deferent temperatures and rotating about a common axis with deferent angular velocities, is considered numerically, when the angular velocities are arbitrary functions of time. The resulting flow pattern, temperature distribution and heat transfer characteristics are presented for the various cases, including exponential and sinusoidal angular velocities. An interesting eject, of long delays in the heat transfer of a large portion of the fluid in the annulus, is observed, because of the angular velocities of the corresponding spheres.