This study deals with natural convective flow of a polar fluid between two concentric open-ended cylinders when the inner surface temperature is higher than the outer or at a constant heat flux. Due to rotation of inner cylinder with angular velocity proportional to gradient of radial/linear velocity with thermal slip at the inner cylinder, a sheared flow is generated. The flow sets in due to momentum as well as thermal energy transport within the annular region. The equations for the velocity, microrotation and temperature fields are solved analytically. There exists a limit to the gap between the cylinders to augment linear velocity as well as microrotation and also a limit to the ratio of vortex viscosity to the dynamic viscosity to override the effects of surface thermal conditions. The thermal slip has an adverse effect on destabilising properties of polar fluid flow.