In the homogeneous Hasegawa–Mima equation, the dipole vortex or modon solution is well known to be robustly stable from both analytic and numerical studies. In the inhomogeneous plasma where∇Te≠0 the corresponding vortex has an external structure extending into the high‐temperature region. Lyapunov stability method is used to determine the stability properties of these extended vortex structures. The overall growth rate of deformation caused by the presence of temperature inhomogeneity is shown to be bounded by (R/LT)2, whereRis the radius of the core of the vortex andLTis the scale length of the temperature gradient. The most important source of instability is identified as the excitation of monopolar and dipolar perturbations with short spatial scales ≲R, which are approximately independent of the presence of the density and temperature gradients.