Industrial practice requires immediate and adequate responses to simple questions asked. For example, does a catalyst particle show any tendency to thermal oscillations in the form of a limit cycle? The root to such cycles is found in the eigenvalues of the Jacobian matrix to the reaction rate vector, applying the concept of reaction invariance, a direct consequence of Avogadro's stoichiometric principle for homogeneous stirred tank reactors. However, this concept does not generally apply to heterogeneous reactor dynamics, because it is found in the heterogeneous transports of heat, reactants and products. The transport is an irreversible phenomenon that usually contributes to shifting the eigenvalues to the left and hence increases the stability. Still, effects of transport mechanisms, both internally and externally, on the catalyst particle are important to assess in such industrial analyses. A practical industrial reactor for methanol production was the subject for stability studies, which concluded that thermal oscillations are not likely to occur. During this study, a number of interesting details were examined such as rank deficiency of the reaction matrix and root loci for the temperature dependence of the Jacobian matrix eigenvalues. A practical consequence of eventual thermal cycling of the catalyst particles is a long-term degradation of the catalyst efficiency, as seen in the ammonia synthesis.