Thermal instabilities, e.g. due to energy losses from impurities, can lead to a sudden drop in the local plasma temperature by orders of magnitude during a time in the micro-second range. A numerical modelling of the global plasma response to such localized phenomena is performed. An approach to calculate with a heat conduction, being a non-linear function both of the temperature and of its gradient, e.g. if the heat flux limit (HFL) is taken into account for plasmas of low collisionality, is developed. It is demonstrated that the deviation of the electron heat conduction from the Spitzer–Härm approximation due to the HFL is essential to explain experimental findings in tokamak experiments with massive gas injection performed to mitigate plasma disruptions.