The influence of an axial convective motion caused by radially nonuniform heat sources on the stability of a Couette flow between cylinders, if the inner one is relating with constant angular velocity and the outer one is fixed, is studied in this paper. The axisymmetric and the first few asymmetric modes are studied. It is found that, for wide gaps, there exist regions of stabilization of Couette flow. These regions, which correspond to asymmetric modes, decrease as the Prandtl number grows.