A numerical solution of linear differential equations governing the stability of the nonaxisymmetric wide‐gap circular Couette flow was present in this study. The numerical solution took into account the presence of a radial temperature gradient between the two rotating cylinders. Boussinesq approximation was applied in the analysis so as to examine the interaction of radial temperature difference with the centrifugal potential but neglect the gravity effect. The critical Taylor number and corresponding critical axial and azimuthal wave numbers were shown graphically for various values of radius ratio, ratio of angular velocities of the inner and outer cylinders, and temperature gradient parameterNfor Prandtl number 0.7. Not only the critical Taylor number but the oscillatory onset mode of nonaxisymmetric disturbances could be altered by the effects of a temperature gradient, as indicated by the calculated results.