A simple non-dimensional model to describe the flutter onset of two-fin straight labyrinth seals  is extended to account for non-isentropic flow perturbations. The isentropic relationship is replaced by the more general integral energy equation of the inter-fin cavity. A new expression for the Corral & Vega stability criterion is derived which is very consistent with the previous model in the whole design space of the seal but for torsion centers located in the high-pressure side close to the seal. The new model formally depends on more dimensionless parameters since the existing parameter grouping of the previous model does not hold anymore, but this dependency is weak in relative terms. The model blends the limit where the discharge time of the inter-fin cavity is much longer than the vibration period, and the flow is nearly isentropic, and the opposite limit, where the perturbations are isothermic, gracefully. A few numerical examples obtained using a three-dimensional linearized frequency domain solver are included to support the model and show that the trends are correct but the body of the numerical work will be presented in a separated article. The matching between the work-per-cycle obtained with the model and frequency domain solver is good. It is shown that some weird trends obtained using linearized unsteady simulations are qualitatively consistent with the current model but not with the previous one . The largest differences between the new and the previous model are seen when the seal is supported at the high-pressure side.