A linear analysis for the instability of viscous flow between two porous concentric circular cylinders driven by a constant azimuthal pressure gradient is presented when a radial flow through the permeable walls of the cylinders is present. In addition, a constant heat flux at the inner cylinder is applied. The linearized stability equations form an eigenvalue problem, which is solved by using the classical Runge–Kutta–Fehlberg scheme combined with a shooting method, which is termed the unit disturbance method. It is found that for a given value of the constant heat flux parameter N, even for a radially weak outward flow, there is a strong stabilizing effect and the stabilization is greater as the gap between the cylinders increases. However, in the presence of a weak inward flow for a wider gap, the constant heat flux has no role on the onset.