Summary: We investigate the steady-state solutions of a nonlinear dynamical system modelling the ignition of thermally thin thermoplastics in the cone calorimeter. The model contains equations for solid phase and gas phase processes which are coupled through heat (convective and radiative) and mass transfer. The existence of different regimes and mechanisms for ignition are demonstrated, and the consequence for fire safety are outlined. The concept of a critical surface temperature defining criticality is validated and a justification is offered.